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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).

Respuesta :

Answer:

p(-2)= 0

p(2)= -16

the value is -2

Step-by-step explanation:


mathjohndough

For any polynomial [tex]f(x)[/tex],  [tex]k[/tex] is a root of the polynomial only if [tex]f(k)=0[/tex] .

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

[tex]p(x)=x^4-9x^2-4x+12[/tex],

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

[tex]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.[/tex]

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

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


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