Q1. If the roots of a quadratic equation are and , find the value of the expression in terms of and hence calculate the value of if .
Q2. Find the value of in the form of where if
Q3. Find the value of in the form of where if
Q4. A quadratic equation is given by
(a) Show that is a root of the equation
(b) Hence, find the other root of the equation.
Q5. Solve the equation , where .
Q6. If and with for the quadratic equation and both roots are real, show that both roots have to be negative.
Q7. The equations and have a common root . Find the value of in terms of .
Q8. Find the values of for which .
Q9. Let the roots of be and roots of be . If are in arithmetic sequence, show that .
Q10. If , has only one solution, show that
Q11. If has roots then find the value of .
Q12. Show that there is no value of for which can have repeated roots.
Q13. If are the roots of the equation , show that the equation with roots is .
Q14. Write the following quadratic function in:
(a) intercept form
(b) vertex form/turning point form
(c) find the zeroes and the vertex of the above quadratic.
Q15. Using the method of completing squares, solve the equation is not equal to
(a) and write the conditions for the above equation to have:
(i) real and distinct roots
(ii) real and equal roots
(iii) no real roots
(b) show that the sum of the roots is given by and product of the roots is
(c) find the solution of when