What are all of the real roots of the following polynomial? f(x) = x4 - 13x2 + 36
2 answers:
ANSWER
A. -3, -2, 2, and 3
EXPLANATION
The given polynomial function is,

To find the real roots, we equate the function to zero to obtain;

We can solve this equation as a quadratic equation in

Thus we rewrite the equation as,

We split the middle term to get,

We factor to get,

We factor to get,

Either

or




The correct answer is A
X^4 - 13x^2 + 36 = 0
(x^2 - 9)(x^2 - 4) = 0
x^2 - 9 = 0 gives x = 3, -3
x^2 - 4 = 0, gives x = 2, -2.
Answer is A.
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