How do you find all the zeros of $F (x) = x^{4} - 13 x^{2} + 36$ $F(x) = x^4 - 13x^2 + 36$ ?

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How do you find all the zeros of $F (x) = x^{4} - 13 x^{2} + 36$ $F(x) = x^4 - 13x^2 + 36$ ?

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Answer 1 · 2016-07-16T21:18:02

Zeros: $\pm 3$ $+-3$ , $\pm 2$ $+-2$

Explanation:

Since there are no terms of odd degree, we can treat this as a quadratic in $x^{2}$ $x^2$ to simplify it, then factorize each of the resulting quadratic factors.

First note that $36 = 9 \times 4$ $36 = 9xx4$ and $9 + 4 = 13$ $9+4=13$ , so we find:

$x^{4} - 13 x^{2} + 36$ $x^4-13x^2+36$

$= {(x^{2})}^{2} - 13 (x^{2}) + 36$ $=(x^2)^2-13(x^2)+36$

$= (x^{2} - 9) (x^{2} - 4)$ $=(x^2-9)(x^2-4)$

$= (x^{2} - 3^{2}) (x^{2} - 2^{2})$ $=(x^2-3^2)(x^2-2^2)$

$= (x - 3) (x + 3) (x - 2) (x + 2)$ $=(x-3)(x+3)(x-2)(x+2)$

Hence zeros:

$\pm 3$ $+-3$ , $\pm 2$ $+-2$

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How do you find all the zeros of $F (x) = x^{4} - 13 x^{2} + 36$ $F(x) = x^4 - 13x^2 + 36$ ?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

How do you find all the zeros of F(x)=x4−13x2+36F(x) = x^4 - 13x^2 + 36?

1 Answer

Explanation:

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How do you find all the zeros of $F (x) = x^{4} - 13 x^{2} + 36$ $F(x) = x^4 - 13x^2 + 36$ ?