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

D

Step-by-step 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