Question

Select all of the following that are potential roots of p(x) = x4 − 9x2 − 4x + 12?

Answer 1

For any polynomial $f(x)$,  $k$ is a root of the polynomial only if $f(k)=0$ .

To determine which of the given values is a root of the polynomial ,

$p(x)=x^4-9x^2-4x+12$,

we just have to evaluate the $f(x)$ for each of these values and see if the output is zero.

$f(-2)=(-2)^4-9(-2)^2-4(-2)+12=16-36+8+12=0.\\f(2)=(2)^4-9(2)^2-4(2)+12=16-36-8+12=-16.$

Since $f(2)=-16$ , we know that $x=2$  is  not a root of this polynomial.

Since $f(-2)=0$ , we know that $x=-2$  is a root of this polynomial.

Answer 2

Answer:

p(-2)= 0

p(2)= -16

the value is -2

Step-by-step explanation: