SOLUTION: The question is to find a polynomial function of 4th degree that has the zeros 2, -2, and 1 - 3i. I got to the part where you turn those into (x-2) (x+2) and (x-1+3i). I think I ha

Algebra ->  Equations -> SOLUTION: The question is to find a polynomial function of 4th degree that has the zeros 2, -2, and 1 - 3i. I got to the part where you turn those into (x-2) (x+2) and (x-1+3i). I think I ha      Log On


   

Question 830133: The question is to find a polynomial function of 4th degree that has the zeros 2, -2, and 1 - 3i. I got to the part where you turn those into (x-2) (x+2) and (x-1+3i). I think I have to multiply them all together, but then I got stucked at the imaginary numbers. They didn't cancel each other out and it seems really wrong. And I don't understand how to put them in standard form afterward with the imaginary number. Can you help me?
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
Q:
Find a polynomial function of 4th degree that has the zeros 2, -2, and 1 - 3i
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A:
The imaginary roots are 1 - 3i and its conjugate which is 1 + 3i.
sum of imaginary roots = (1 - 3i) + (1 + 3i) = 2
product of imaginary roots = (1 - 3i)(1 + 3i) = 10
Quadratic equation: x%5E2+-+%28sum%29x+%2B+product+=+0
x%5E2+-+2x+%2B+10+=+0
The real roots are 2 and -2
Quadratic Equation: (x + 2)(x - 2) = 0 or x%5E2+-+4+=+0.
Fourth degree polynomial equation: %28x%5E2-2x%2B10%29%28x%5E2-4%29+=+0 or
x%5E4+-+2x%5E3+%2B+6x%5E2+%2B+8x+-+40+=+0
The polynomial function is highlight%28f%28x%29+=+x%5E4+-+2x%5E3+%2B+6x%5E2+%2B+8x+-+40%29.