Question

Find a polynomial function of degree 3 with -1, 2, 4 as zeros

Answer 1

f(x) = x³ - 5x² + 2x + 8

Explanation:

given the zeros of a polynomial, say x = a and x = b, then

(x - a) and (x - b) are the factors and the polynomial is the product of the factors.

here x = - 1, x = 2 and x = 4 are zeros, hence

(x + 1), (x - 2) and (x - 4) are the factors

f(x) = a(x + 1)(x - 2)(x - 4) ( a is a multiplier )

let a = 1, then expanding factors

f(x) = (x + 1)(x² - 6x + 8) = x³ - 5x² + 2x + 8