{"id":562,"date":"2020-01-26T15:06:47","date_gmt":"2020-01-26T15:06:47","guid":{"rendered":"http:\/\/localhost\/?post_type=knowledgebase&#038;p=562"},"modified":"2020-03-24T03:43:43","modified_gmt":"2020-03-24T03:43:43","slug":"practise-questions-quadratics","status":"publish","type":"knowledgebase","link":"https:\/\/ibalmaths.com\/index.php\/ibdp-math-hl-2\/quadratics\/practise-questions-quadratics\/","title":{"rendered":"Quadratics &#8211; Practice questions"},"content":{"rendered":"<p style=\"text-align: left;\"><strong>Q1<\/strong>. If the roots of a quadratic equation\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>2<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mn>3<\/mn><mi>x<\/mi><mo>&#8211;<\/mo><mi>k<\/mi><mo>=<\/mo><mn>0<\/mn><\/math>\r\n are \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>tan<\/mi><mi>&#945;<\/mi><\/math>\r\n \u00a0and\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>tan<\/mi><mi>&#946;<\/mi><\/math>\r\n , find the value of the expression\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>tan<\/mi><mfenced><mrow><mi>&#945;<\/mi><mo>+<\/mo><mi>&#946;<\/mi><\/mrow><\/mfenced><\/math>\r\n \u00a0in terms of\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>k<\/mi><\/math>\r\n and hence calculate the value of \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>k<\/mi><\/math>\r\n if\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>&#945;<\/mi><mo>+<\/mo><mi>&#946;<\/mi><mo>=<\/mo><mfrac><mrow><mn>3<\/mn><mi>&#960;<\/mi><\/mrow><mn>4<\/mn><\/mfrac><\/math>\r\n .\u00a0<\/p>\r\n<p style=\"text-align: left;\"><div id=\"link1-link-562\" class=\"sh-link link1-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link1', 562, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link1-toggle-562\">Solution<\/span><\/a><\/div><div id=\"link1-content-562\" class=\"sh-content link1-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p style=\"text-align: left;\">coming soon<br \/>\r\n<\/div><\/p>\r\n<p style=\"text-align: left;\"><strong>Q2<\/strong>. Find the value of \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>x<\/mi><\/math>\r\n in the form of\u00a0\u00a0\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mrow><mi>a<\/mi><mo>+<\/mo><msqrt><mi>b<\/mi><\/msqrt><\/mrow><mi>c<\/mi><\/mfrac><\/math>\r\n where\u00a0\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><mo>,<\/mo><mi>b<\/mi><mo>,<\/mo><mi>c<\/mi><mo>&#8712;<\/mo><mi mathvariant=\"normal\">&#8484;<\/mi><\/math>\r\n if<\/p>\r\n<p>\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>x<\/mi><mo>=<\/mo><msqrt><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mo>+<\/mo><msqrt><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mo>+<\/mo><msqrt><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mo>+<\/mo><msqrt><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mo>+<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><\/msqrt><\/msqrt><\/msqrt><\/msqrt><\/math>\r\n<\/p>\r\n<p style=\"text-align: left;\"><div id=\"link2-link-562\" class=\"sh-link link2-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link2', 562, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link2-toggle-562\">Solution<\/span><\/a><\/div><div id=\"link2-content-562\" class=\"sh-content link2-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p style=\"text-align: left;\">coming soon<br \/>\r\n<\/div><\/p>\r\n<p style=\"text-align: left;\"><strong>Q3<\/strong>. Find the value of\u00a0\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>x<\/mi><\/math>\r\n in the form of \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><mo>+<\/mo><msqrt><mi>b<\/mi><\/msqrt><\/math>\r\n where\u00a0\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><mo>,<\/mo><mo>&#160;<\/mo><mi>b<\/mi><mo>&#8712;<\/mo><mi mathvariant=\"normal\">&#8484;<\/mi><\/math>\r\n if\u00a0<\/p>\r\n<p>\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>x<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>2<\/mn><mo>+<\/mo><mstyle displaystyle=\"true\"><mfrac><mn>1<\/mn><mrow><mn>2<\/mn><mo>+<\/mo><mstyle displaystyle=\"true\"><mfrac><mn>1<\/mn><mrow><mn>2<\/mn><mo>+<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><\/mrow><\/mfrac><\/mstyle><\/mrow><\/mfrac><\/mstyle><\/mrow><\/mfrac><\/math>\r\n<\/p>\r\n<p style=\"text-align: left;\"><div id=\"link3-link-562\" class=\"sh-link link3-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link3', 562, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link3-toggle-562\">Solution<\/span><\/a><\/div><div id=\"link3-content-562\" class=\"sh-content link3-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p style=\"text-align: left;\">coming soon<br \/>\r\n<\/div><\/p>\r\n<p style=\"text-align: left;\"><strong>Q4<\/strong>. A quadratic equation is given by\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfenced><mrow><mi>b<\/mi><mo>&#8211;<\/mo><mi>c<\/mi><\/mrow><\/mfenced><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mfenced><mrow><mi>c<\/mi><mo>&#8211;<\/mo><mi>a<\/mi><\/mrow><\/mfenced><mi>x<\/mi><mo>+<\/mo><mi>a<\/mi><mo>&#8211;<\/mo><mi>b<\/mi><mo>=<\/mo><mn>0<\/mn><mo>,<\/mo><\/math>\r\n<\/p>\r\n<p style=\"text-align: left;\">(a) Show that\u00a0\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>x<\/mi><mo>=<\/mo><mn>1<\/mn><\/math>\r\n is a root of the equation<\/p>\r\n<p style=\"text-align: left;\">(b)\u00a0Hence, find the other root of the equation.<\/p>\r\n<p style=\"text-align: left;\"><div id=\"link4-link-562\" class=\"sh-link link4-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link4', 562, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link4-toggle-562\">Solution<\/span><\/a><\/div><div id=\"link4-content-562\" class=\"sh-content link4-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p style=\"text-align: left;\">coming soon<br \/>\r\n<\/div><\/p>\r\n<p style=\"text-align: left;\"><strong>Q5<\/strong>. Solve the equation \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>x<\/mi><mrow><mn>6<\/mn><mo>\/<\/mo><mn>5<\/mn><\/mrow><\/msup><mo>&#8211;<\/mo><mn>9<\/mn><msup><mi>x<\/mi><mrow><mn>3<\/mn><mo>\/<\/mo><mn>5<\/mn><\/mrow><\/msup><mo>+<\/mo><mn>8<\/mn><mo>=<\/mo><mn>0<\/mn><\/math>\r\n, where \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>x<\/mi><mo>&#8712;<\/mo><mi mathvariant=\"normal\">&#8484;<\/mi><\/math>\r\n.<\/p>\r\n<p style=\"text-align: left;\"><div id=\"link5-link-562\" class=\"sh-link link5-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link5', 562, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link5-toggle-562\">Solution<\/span><\/a><\/div><div id=\"link5-content-562\" class=\"sh-content link5-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p style=\"text-align: left;\">coming soon<br \/>\r\n<\/div><\/p>\r\n<p style=\"text-align: left;\"><strong>Q6<\/strong>. If\u00a0\u00a0\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><mo>&#62;<\/mo><mn>0<\/mn><mo>,<\/mo><mo>&#160;<\/mo><mi>b<\/mi><mo>&#62;<\/mo><mn>0<\/mn><\/math>\r\n\u00a0and\u00a0\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>c<\/mi><mo>&#62;<\/mo><mn>0<\/mn><\/math>\r\n with\u00a0\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><mo>,<\/mo><mo>&#160;<\/mo><mi>b<\/mi><mo>,<\/mo><mo>&#160;<\/mo><mi>c<\/mi><mo>&#8712;<\/mo><mi mathvariant=\"normal\">&#8477;<\/mi><\/math>\r\n for the quadratic equation \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mi>b<\/mi><mi>x<\/mi><mo>+<\/mo><mi>c<\/mi><mo>=<\/mo><mn>0<\/mn><\/math>\r\n and both roots are real, show that both roots have to be negative.<\/p>\r\n<p style=\"text-align: left;\"><div id=\"link6-link-562\" class=\"sh-link link6-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link6', 562, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link6-toggle-562\">Solution<\/span><\/a><\/div><div id=\"link6-content-562\" class=\"sh-content link6-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p style=\"text-align: left;\">coming soon<br \/>\r\n<\/div><\/p>\r\n<p style=\"text-align: left;\"><strong>Q7<\/strong>. The equations \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mi>x<\/mi><mo>+<\/mo><mi>k<\/mi><mo>=<\/mo><mn>0<\/mn><\/math>\r\n\u00a0and\u00a0\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>k<\/mi><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>&#8211;<\/mo><mn>2<\/mn><mi>k<\/mi><mi>x<\/mi><mo>+<\/mo><mn>1<\/mn><mo>=<\/mo><mn>0<\/mn><\/math>\r\n have a common root \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>&#945;<\/mi><\/math>\r\n. Find the value of \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>&#945;<\/mi><\/math>\r\n\u00a0in terms of\u00a0\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>k<\/mi><\/math>\r\n.<\/p>\r\n<p style=\"text-align: left;\"><div id=\"link7-link-562\" class=\"sh-link link7-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link7', 562, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link7-toggle-562\">Solution<\/span><\/a><\/div><div id=\"link7-content-562\" class=\"sh-content link7-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p style=\"text-align: left;\">coming soon<br \/>\r\n<\/div><\/p>\r\n<p style=\"text-align: left;\"><strong>Q8<\/strong>.\u00a0Find the values\u00a0\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>k<\/mi><\/math>\r\n\u00a0of for which\u00a0\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mi>x<\/mi><mo>+<\/mo><mi>k<\/mi><mo>&#8805;<\/mo><mn>0<\/mn><\/math>\r\n.<\/p>\r\n<p style=\"text-align: left;\"><div id=\"link8-link-562\" class=\"sh-link link8-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link8', 562, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link8-toggle-562\">Solution<\/span><\/a><\/div><div id=\"link8-content-562\" class=\"sh-content link8-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p style=\"text-align: left;\">coming soon<br \/>\r\n<\/div><\/p>\r\n<p style=\"text-align: left;\"><strong>Q9<\/strong>.\u00a0Let the roots of\u00a0\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>l<\/mi><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mi>m<\/mi><mi>x<\/mi><mo>+<\/mo><mi>n<\/mi><mo>=<\/mo><mn>0<\/mn><\/math>\r\n be\u00a0\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>&#945;<\/mi><mo>,<\/mo><mo>&#160;<\/mo><mi>&#946;<\/mi><\/math>\r\n\u00a0and roots of\u00a0\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mi>b<\/mi><mi>x<\/mi><mo>+<\/mo><mi>c<\/mi><mo>=<\/mo><mn>0<\/mn><\/math>\r\n be\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>&#947;<\/mi><mo>,<\/mo><mo>&#160;<\/mo><mi>&#948;<\/mi><\/math>\r\n. If\u00a0\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>&#945;<\/mi><mo>,<\/mo><mo>&#160;<\/mo><mi>&#946;<\/mi><mo>,<\/mo><mo>&#160;<\/mo><mi>&#947;<\/mi><mo>,<\/mo><mo>&#160;<\/mo><mi>&#948;<\/mi><\/math>\r\n\u00a0are in arithmetic sequence, show that\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mrow><msup><mi>b<\/mi><mn>2<\/mn><\/msup><mo>&#8211;<\/mo><mo>&#160;<\/mo><mn>4<\/mn><mi>a<\/mi><mi>c<\/mi><\/mrow><msup><mi>a<\/mi><mn>2<\/mn><\/msup><\/mfrac><mo>=<\/mo><mfrac><mrow><msup><mi>m<\/mi><mn>2<\/mn><\/msup><mo>&#8211;<\/mo><mo>&#160;<\/mo><mn>4<\/mn><mi>n<\/mi><mi>l<\/mi><\/mrow><msup><mi>l<\/mi><mn>2<\/mn><\/msup><\/mfrac><\/math>\r\n.<\/p>\r\n<p style=\"text-align: left;\"><div id=\"link9-link-562\" class=\"sh-link link9-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link9', 562, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link9-toggle-562\">Solution<\/span><\/a><\/div><div id=\"link9-content-562\" class=\"sh-content link9-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p style=\"text-align: left;\">coming soon<br \/>\r\n<\/div><\/p>\r\n<p style=\"text-align: left;\"><strong>Q10<\/strong>. If\u00a0\u00a0\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>x<\/mi><mo>+<\/mo><mi>k<\/mi><mi>y<\/mi><mo>=<\/mo><mn>1<\/mn><\/math>\r\n,\u00a0\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mi>b<\/mi><msup><mi>y<\/mi><mn>2<\/mn><\/msup><mo>=<\/mo><mn>1<\/mn><\/math>\r\n has only one solution, show that \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>b<\/mi><mo>=<\/mo><mfrac><mrow><mi>a<\/mi><msup><mi>k<\/mi><mn>2<\/mn><\/msup><\/mrow><mrow><mi>a<\/mi><mo>&#160;<\/mo><mo>&#8211;<\/mo><mo>&#160;<\/mo><mn>1<\/mn><\/mrow><\/mfrac><\/math>\r\n<\/p>\r\n<p style=\"text-align: left;\"><div id=\"link10-link-562\" class=\"sh-link link10-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link10', 562, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link10-toggle-562\">Solution<\/span><\/a><\/div><div id=\"link10-content-562\" class=\"sh-content link10-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p style=\"text-align: left;\">coming soon<br \/>\r\n<\/div><\/p>\r\n<p style=\"text-align: left;\"><strong>Q11<\/strong>. If \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mn>2<\/mn><mi>x<\/mi><mo>&#8211;<\/mo><mi>k<\/mi><mo>=<\/mo><mn>0<\/mn><\/math>\r\n has roots\u00a0\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>sin<\/mi><mi>&#945;<\/mi><mo>,<\/mo><mo>&#160;<\/mo><mi>cos<\/mi><mi>&#945;<\/mi><\/math>\r\n then find the value of \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>k<\/mi><\/math>\r\n\u00a0.<\/p>\r\n<p style=\"text-align: left;\"><div id=\"link11-link-562\" class=\"sh-link link11-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link11', 562, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link11-toggle-562\">Solution<\/span><\/a><\/div><div id=\"link11-content-562\" class=\"sh-content link11-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p style=\"text-align: left;\">coming soon<br \/>\r\n<\/div><\/p>\r\n<p style=\"text-align: left;\"><strong>Q12<\/strong>. Show that there is no value of\u00a0\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><\/math>\r\nfor which \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mfenced><mrow><mi>x<\/mi><mo>&#8211;<\/mo><mi>a<\/mi><\/mrow><\/mfenced><mn>2<\/mn><\/msup><mo>+<\/mo><mn>1<\/mn><mo>=<\/mo><mn>0<\/mn><\/math>\r\n can have repeated roots.\u00a0<\/p>\r\n<p style=\"text-align: left;\"><div id=\"link12-link-562\" class=\"sh-link link12-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link12', 562, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link12-toggle-562\">Solution<\/span><\/a><\/div><div id=\"link12-content-562\" class=\"sh-content link12-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p style=\"text-align: left;\">coming soon<br \/>\r\n<\/div><\/p>\r\n<p style=\"text-align: left;\"><strong>Q13<\/strong>. If \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>&#945;<\/mi><mo>,<\/mo><mo>&#160;<\/mo><mi>&#946;<\/mi><\/math>\r\n are the roots of the equation\u00a0, show that the equation with roots \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>&#945;<\/mi><mo>+<\/mo><mi>k<\/mi><mo>,<\/mo><mo>&#160;<\/mo><mi>&#946;<\/mi><mo>+<\/mo><mi>k<\/mi><\/math>\r\n is \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>&#8211;<\/mo><mi>k<\/mi><mi>x<\/mi><mo>&#8211;<\/mo><mn>1<\/mn><mo>=<\/mo><mn>0<\/mn><\/math>\r\n.<\/p>\r\n<p style=\"text-align: left;\"><div id=\"link13-link-562\" class=\"sh-link link13-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link13', 562, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link13-toggle-562\">Solution<\/span><\/a><\/div><div id=\"link13-content-562\" class=\"sh-content link13-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p style=\"text-align: left;\">coming soon<br \/>\r\n<\/div><\/p>\r\n<p style=\"text-align: left;\"><strong>Q14<\/strong>. Write the following quadratic function\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>f<\/mi><mfenced><mi>x<\/mi><\/mfenced><mo>=<\/mo><mn>6<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mn>5<\/mn><mi>x<\/mi><mo>&#8211;<\/mo><mn>6<\/mn><\/math>\r\n\u00a0in:\u00a0<\/p>\r\n<p style=\"text-align: left;\">(a) intercept form<\/p>\r\n<p style=\"text-align: left;\">(b) vertex form\/turning point form<\/p>\r\n<p style=\"text-align: left;\">(c)\u00a0find the zeroes and the vertex of the above quadratic.<\/p>\r\n<p style=\"text-align: left;\"><div id=\"link14-link-562\" class=\"sh-link link14-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link14', 562, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link14-toggle-562\">Solution<\/span><\/a><\/div><div id=\"link14-content-562\" class=\"sh-content link14-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p style=\"text-align: left;\">coming soon<br \/>\r\n<\/div><\/p>\r\n<p style=\"text-align: left;\"><strong>Q15<\/strong>. Using the method of completing squares, solve the equation\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mi>b<\/mi><mi>x<\/mi><mo>+<\/mo><mi>c<\/mi><mo>=<\/mo><mn>0<\/mn><mo>,<\/mo><mo>&#160;<\/mo><mo>&#160;<\/mo><mi>a<\/mi><\/math>\r\n is not equal to\u00a0\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>0<\/mn><\/math>\r\n<\/p>\r\n<p style=\"text-align: left;\">(a)\u00a0and write the conditions for the above equation to have:<\/p>\r\n<p style=\"text-align: left;\">(i)\u00a0real and distinct roots<\/p>\r\n<p style=\"text-align: left;\">(ii)\u00a0real and equal roots<\/p>\r\n<p style=\"text-align: left;\">(iii)\u00a0no real roots<\/p>\r\n<p style=\"text-align: left;\">(b) show that the sum of the roots is given by \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>&#8211;<\/mo><mfrac><mi>b<\/mi><mi>a<\/mi><\/mfrac><\/math>\r\n\u00a0and product of the roots is\u00a0\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mi>c<\/mi><mi>a<\/mi><\/mfrac><\/math>\r\n<\/p>\r\n<p style=\"text-align: left;\">(c) find the solution of\u00a0\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mi>b<\/mi><mi>x<\/mi><mo>+<\/mo><mi>c<\/mi><mo>&#8804;<\/mo><mn>0<\/mn><\/math>\r\n\u00a0when<\/p>\r\n<p style=\"text-align: left;\">(i)\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><mo>&#60;<\/mo><mn>0<\/mn><\/math>\r\n<\/p>\r\n<p style=\"text-align: left;\">(ii)\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><mo>&#62;<\/mo><mn>0<\/mn><mo>.<\/mo><\/math>\r\n<\/p>\r\n<p style=\"text-align: left;\"><div id=\"link15-link-562\" class=\"sh-link link15-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link15', 562, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link15-toggle-562\">Solution<\/span><\/a><\/div><div id=\"link15-content-562\" class=\"sh-content link15-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p style=\"text-align: left;\">coming soon<br \/>\r\n<\/div><\/p><!-- AddThis Advanced Settings generic via filter on the_content --><!-- AddThis Share Buttons generic via filter on the_content -->","protected":false},"excerpt":{"rendered":"Q1. If the roots of a quadratic equation\u00a0 2&#215;2+3x&#8211;k=0 are tan&#945; \u00a0and\u00a0 tan&#946; , find the value of the expression\u00a0 tan&#945;+&#946; \u00a0in terms of\u00a0 k and hence calculate the value of k if\u00a0 &#945;+&#946;=3&#960;4 .\u00a0 Q2. Find the value of x in the form of\u00a0\u00a0 a+bc where\u00a0 a,b,c&#8712;&#8484; if x=12+12+12+12+&#8230;&#8230;&#8230;. Q3. Find the value of\u00a0 [&hellip;]<!-- AddThis Advanced Settings generic via filter on get_the_excerpt --><!-- AddThis Share Buttons generic via filter on get_the_excerpt -->","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-562","knowledgebase","type-knowledgebase","status-publish","hentry","knowledgebase_cat-quadratics","no-wpautop"],"_links":{"self":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/562","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase"}],"about":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/types\/knowledgebase"}],"author":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/comments?post=562"}],"version-history":[{"count":29,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/562\/revisions"}],"predecessor-version":[{"id":1407,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/562\/revisions\/1407"}],"wp:attachment":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/media?parent=562"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}