Question

Find a polynomial equation that has zeros at x = -4, x = 0, and a double root at x = 7.

A)
y = (x + 4)(x – 7)
B)
y = 2x(x + 4)(x – 7)
c)
y = (x + 4)(x)(x – 7)
D)
y = x(x + 4)(x – 7)2

Answer 1

D

Explanation:

Given a polynomial f(x) with roots say x = a and x = b, then the factors are

(x - a) and (x - b) and f(x) is the product of the roots, that is

f(x) = (x - a)(x - b)

Here the roots are x = - 4, x = 0 and double root at x = 7

Thus factors are (x - (- 4)), (x - 0), that is (x + 4) and x

Given a double root at x = 7 the factor is (x - 7)², thus polynomial is

y = x(x + 4)(x - 7)² → D