Question

Which of the following is a polynomial with roots 4, -5, and 7?

A. f(x) = x^3 - 6x - 27x + 140
B. f(x) = x^3 - 6x - 20x + 27
C. f(x) = x^3 - 20x^2 - 27x + 35
D. f(x) = x^3 - 20x^2 - 35x + 140

Answer 1

A

Explanation:

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

(x - a), (x - b) and (x - c) are it's factors and the polynomial is the product of it's factors.

here the roots are x = 4, x = - 5 and x = 7, hence

(x - 4), (x + 5) and (x - 7) are the factors

f(x) = a(x - 4)(x + 5)(x - 7) ← a is a multiplier

let a = 1 and expand the factors

f(x) = (x² + x - 20)(x - 7)

= x³ + x² - 20x - 7x² - 7x + 140

= x³ - 6x² - 27x + 140 → A