SOLUTION: find the complex zeros of the polynomial function f(x)=x^4+23x^2+22 write f in factored form f(x)= please show step by step work i am very confused.

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Question 964458: find the complex zeros of the polynomial function f(x)=x^4+23x^2+22
write f in factored form f(x)=
please show step by step work i am very confused.
Found 2 solutions by rothauserc, josmiceli:
Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website!
f(x) = x^4 +23x^2 +22
first write down the factors of 22, they are
1, 22
2, 11
now 1 and 22 look promising since the coefficient of x^2 is 23
let's try
(x^2 +1) * (x^2 +22) = x^4 +23x^2 + 22
we can now write the solutions for x as
x^2 = -1
x = sqrt(-1) = i
x^2 = -22
x = sqrt(-22) = i*sqrt(22)
therefore our 2 solutions for x are
x = i and x = i*sqrt(22)

Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
here's how I would do it:

Let
Substituting:

I can see that the factors for
finding roots

The solutions for are:

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So, now I can say:

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The 4 factors of are:

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check:

and

and

OK