4.8# 31, 41
I'm having trouble getting rid of the complex part of the polynomial when i expand an expression based on the roots. Any suggestions on where to go after writing an expression for the polynimial based on the given roots?
posted by Carrie Desmond at 6:49 PM
1 Comments:
If the factors of a quadratic are (x-r) and (x-s), the polynomial can be written: f(x)=x^2-(r+s)x+r*s. If you have a complex number as a root of a quadratic, you know that its conjugate will also be a root, so you can call these complex numbers r and s. So if r was 1-i, s could be 1+i. The polynomial would then be x^2-(1-i+1+i)x+(1+i)(1-i)=x^2-2x+(1-i^2)=x^2-2x+2.
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