Saturday, July 6, 2013

Form a polynomial f(x)with real coefficients having the given degrees and zeros. Degree: 4 Zero's: -4+3i; -5 multiplicity 2

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... 


f%28x%29=%28x-%28-4%2B3i%29%29%28x-%28-4-3i%29%29%28x-%28-5%29%29%5E2 
and after multiplying ( it's tedious but not hard) we get 


f%28x%29+=+x%5E4%2B18x%5E3%2B130x%5E2%2B450x%2B625


:)

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