Form a polynomial f(x) with real coefficients...question
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Form a polynomial f(x) with real coefficients...question

[From: ] [author: ] [Date: 12-04-26] [Hit: ]
Those pairs give you first (x+2i)(x+2i)= (x^2 +4) as a factor of f; then similarly, (x^2 +25) is a factor.......
Degree: 4; zeros: 2i and -5i

I know the answer is f(x)=x^4+29x^2+100 but i would like to know see the steps and how to figure it out
thank you!

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If it has real coefficients, then the complex roots must come in pairs of complex conjugates. (You probably already know that the complex conjugate of a+bi = a -bi, and the complex conjugate of ci = +ci.) That means that if 2i is a root, -2i must also be a root. And -5i gives you 5i as another required root.

Those pairs give you first (x+2i)(x+2i)= (x^2 +4) as a factor of f; then similarly, (x^2 +25) is a factor.

Multiply those and you get x^4 + 29x^2 + 100
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