SOLUTION: Form a polynomial f left parenthesis x right parenthesis with real coefficients having the given degree and zeros.
Degree 4; zeros: 3+2i ; -5 multiplicity 2
Enter the pol
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Question 1157331: Form a polynomial f left parenthesis x right parenthesis with real coefficients having the given degree and zeros.
Degree 4; zeros: 3+2i ; -5 multiplicity 2
Enter the polynomial.
f(x)=a(___)
Answer by greenestamps(13334) (Show Source): You can put this solution on YOUR website!
The polynomial is to have real coefficients, so the complex zeros occur in conjugate pairs. So the roots are 3+2i, 3-2i, -5, and -5.
Use Vieta's theorem to find the quadratic polynomial with roots 3+2i and 3-2i:
The quadratic polynomial is
The quadratic polynomial with roots -5 and -5 is
The polynomial we want is
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