Examples of Math Problems: Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 5; zeros: 9, -i, -8+i

Tuesday, June 11, 2013

Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 5; zeros: 9, -i, -8+i

The general polynomial with these roots is:
%0D%0Ap%28x%29=a%28x-9%29%28x%2Bi%29%28x-i%29%28x-%28-8-i%29%29%28x-%28-8%2Bi%29%29%0D%0A

%0D%0Ap%28x%29=a%28x-9%29%28x%2Bi%29%28x-i%29%28x-%28-8-i%29%29%28x-%28-8%2Bi%29%29%0D%0A

let a=1, then

%0D%0Ap%28x%29=%28x-9%29%28x%5E2%2B1%29%28x%5E2%2B16x%2B65%29%0D%0A

%0D%0Ap%28x%29=%28x-9%29%28x%5E2%2B1%29%28x%5E2%2B16x%2B65%29%0D%0A

%0D%0Ap%28x%29=x%5E5%2B7x%5E4-78+x%5E3-578+x%5E2-79+x-585%0D%0A

:)

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