SOLUTION: write a polynomial function of least degree with integral coefficients that has the given zeros: -2, i, -i

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Question 1023529: write a polynomial function of least degree with integral coefficients that has the given zeros: -2, i, -i
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given zeros: x%5B1%5D=-2, x%5B2%5D=i, x%5B3%5D=-i
f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29
f%28x%29=%28x-%28-2%29%29%28x-i%29%28x-%28-i%29%29
f%28x%29=%28x%2B2%29%28x-i%29%28x%2Bi%29
f%28x%29=%28x%2B2%29%28x%5E2-%28i%29%5E2%29
f%28x%29=%28x%2B2%29%28x%5E2-%28-1%29%29
f%28x%29=%28x%2B2%29%28x%5E2%2B1%29
f%28x%29=x%5E2%2Ax%2B1%2Ax%2Bx%5E2%2A2%2B1%2A2
f%28x%29=x%5E3%2B2x%5E2%2Bx%2B2

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E3%2B2x%5E2%2Bx%2B2%29+