Question

Which statement best describes the zeros of the function h(x) = (x – 6)(x2 + 8x + 16)? A. The function has two distinct real zeros. B. The function has three distinct real zeros. C. The function has one real zero and two complex zeros. D. The function has three complex zeros.

Answer 1

Answer:

A

Step-by-step explanation:

Here, we want to choose the option that best suit the question.

Let’s consider the cases individually;

for (x-6) = 0

we have a root at x = 6 which is a real root

Secondly

x^2 + 8x + 16 = x^2 + 4x + 4x + 16 = 0

That would be;

x(x + 4) + 4(x + 4)

(x + 4)(x + 4) = 0

Thus x = - 4 twice

So the roots of the given equation would be;

6 , -4 , -4

Which is 3 real roots but only 2 real distinct roots