Question

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

Evaluate the function for the given values to determine if the value is a root.

p(−2) =

p(2) =

The value is a root of p(x).

Answer 1

p(-2)= 0

p(2)= -16

the value is -2

Explanation:

Answer 2

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.