SOLUTION: Find the Polynomial P(x)having real coefficents, with the degree and zeros indicated. Assume the lead coefficient is 1. Recall (a+bi)(a-bi)=a^2 + b^2. degree 4, x- -7, x=9, x= -6i.

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Find the Polynomial P(x)having real coefficents, with the degree and zeros indicated. Assume the lead coefficient is 1. Recall (a+bi)(a-bi)=a^2 + b^2. degree 4, x- -7, x=9, x= -6i.      Log On


   

Question 319281: Find the Polynomial P(x)having real coefficents, with the degree and zeros indicated. Assume the lead coefficient is 1. Recall (a+bi)(a-bi)=a^2 + b^2. degree 4, x- -7, x=9, x= -6i.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Since x=-6i is a zero, x=6i is also a root.
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f%28x%29=%28x%2B7%29%28x-9%29%28x-6i%29%28x%2B6i%29
f%28x%29=%28x%5E2-2x-63%29%28x%5E2%2B36%29
f%28x%29=%28x%5E2-2x-63%29%28x%5E2%29%2B%28x%5E2-2x-63%29%2836%29
f%28x%29=%28x%5E4-2x%5E3-63x%5E2%29%2B%2836x%5E2-72x-2268%29
f%28x%29=x%5E4-2x%5E3-27x%5E2-72x-2268