IBDP Past Year Exam Questions 2- Polynomials

1675 April 6, 2020

1.[M14/P1/TZ1]

When the polynomial $3 x^{3} + a x + b$ is divided by $(x - 2)$ , the remainder is 2, and when divided by $(x + 1)$ , it is 5. Find the value of a and the value of b . [5 marks]

Solution

2.[M14/P1/TZ1]

The equation $5 x^{3} + 48 x^{2} + 100 x + 2 = a$ has roots $r_{1}, r_{2}$ and $r_{3}$ . Given that $r_{1} + r_{2} + r_{3} + r_{1} r_{2} r_{3} = 0$ , find the value of a . [6 marks]

Solution