Question

eWhat are the zeros of the function f(x) = (2x+6)(x-4)?OA. x = 6 and x = -4OB. x=-6 and x = -4OC. x=3 and x = -4OD. x=-3 and x = 4

Answer 1

Hello there. To solve this question, we have to remember some properties about roots of polynomials.

Given the following function:

$f(x)=(2x+6)\cdot(x-4)$

We want to determine its roots.

For this, we want to determine the values of x such that

$f(x)=0$

Then we have that

$(2x+6)\cdot(x-4)=0$

We know that a product of two values is equal to zero if and only if one of them is equal to zero.

So we have that

$2x+6=0\text{ or }x-4=0$

Subtract 6 on both sides of the first equation, we get

$2x=-6$

Divide both sides of the equation by a factor of 2

$x=-3$

Now for the second equation, add 4 on both sides of the equation

$x=4$

Hence we say that the roots of this function are

$x=-3\text{ and }x=4$

This is the answer contained in the last option.