Question

Find the equation of a polynomial with the zeros 8, 5, 1, and -1.

Answer 1

f(x) = x⁴ - 13x³ + 39x² + 13x - 40

Explanation:

If the zeroes are 8, 5, 1 and -1, then x = 8, x = 5, x = 1, x = -1

⇒ x - 8 = 0

⇒ x - 5 = 0

⇒ x - 1 = 0

⇒ x + 1 = 0

⇒ f(x) = (x - 8)(x - 5)(x - 1)(x + 1)

⇒ f(x) = x⁴ - 13x³ + 39x² + 13x - 40