SOLUTION: what is fourth degree polynomial with the interger coeffients that has zeros 3i and -1 ,-1 has multiplicity of 2?

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Question 1130350: what is fourth degree polynomial with the interger coeffients that has zeros 3i and -1 ,-1 has multiplicity of 2?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

zeros:
x%5B1%5D=+3i=> there is also x%5B2%5D=+-3i (complex roots always come in pairs)
x%5B3%5D=-1 ,-1 has multiplicity of 2

f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29%5E2
f%28x%29=%28x-3i%29%28x-%28-3i%29%29%28x-%28-1%29%29%5E2
f%28x%29=%28x-3i%29%28x%2B3i%29%28x%2B1%29%5E2
f%28x%29=%28x%5E2-%283i%29%5E2%29%28x%5E2%2B2x%2B1%29
f%28x%29=%28x%5E2-9i%5E2%29%28x%5E2%2B2x%2B1%29
f%28x%29=%28x%5E2-9%28-1%29%29%28x%5E2%2B2x%2B1%29
f%28x%29=%28x%5E2%2B9%29%28x%5E2%2B2x%2B1%29
f%28x%29=x%5E4+%2B+2x%5E3+%2B+10x%5E2+%2B+18x+%2B+9