SOLUTION: Form a polynomial f(x)with real coefficients having the given degree and zeros. Degree 5 and Zeros -1, -i,-4+i What is f(x)?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Form a polynomial f(x)with real coefficients having the given degree and zeros. Degree 5 and Zeros -1, -i,-4+i What is f(x)?      Log On


   

Question 764936: Form a polynomial f(x)with real coefficients having the given degree and zeros. Degree 5 and Zeros -1, -i,-4+i What is f(x)?
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
Since the coefficients are real, the complex zeros must occur in conjugate pairs, and the multiplicity of a zero tells how many times it occurs, so...

%0D%0Af%28x%29=%28x-%28-1%29%29%28x-i%29%28x%2Bi%29%28x%2B4-i%29%28x%2B4%2Bi%29%0D%0A

and after multiplying ( it's tedious but not hard) we get

%0D%0Af%28x%29=x%5E5%2B9x%5E4%2B26x%5E3%2B26x%5E2%2B25x%2B17%0D%0A

:)