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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).

2 Answers

3 votes

Answer:

p(-2)= 0

p(2)= -16

the value is -2

Explanation:


User Jenko
by
9.0k points
4 votes

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.


User Npinti
by
8.0k points