Question

If 1 and -1 are the zeroes of the polynomial p(x) = ax 3 + x 2 − 2x + b, find the values of a and b

Answer 1

a = 2, b = -1

Explanation:

p(x) = ax³ + x² - 2x + b

p(1) = a(1)³ + 1² - 2•1 + b = a + 1 - 2 + b = a + b - 1

a + b - 1 = 0 ⇒ b = 1 - a

p(-1) = a(-1)³ + (-1)² - 2(-1) + b = -a + 1 + 2 + b = - a + b + 3

- a + b + 3 = 0 ∧ b = 1 - a

- a + (1 - a) + 3 = 0

- a + 1 - a + 3 = 0

-2a + 4 = 0

-2a = -4

a = 2

b = 1 - 2 = -1