SOLUTION: Write a polynomial fx that satisfies the given conditions. Degree 3 polynomial with integer coefficients with zeros −5i and 6/5

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Question 1154787: Write a polynomial fx
that satisfies the given conditions.
Degree 3
polynomial with integer coefficients with zeros −5i
and 6/5

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
Degree 3
polynomial with integer coefficients
with zeros:
x%5B1%5D=-5i=> complex zeros always come in pairs, so you also have x%5B2%5D=5i
and
x%5B3%5D=6%2F5
f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29
f%28x%29=%28x-%28-5i%29%29%28x-5i%29%28x-6%2F5%29
f%28x%29=%28x%2B5i%29%28x-5i%29%28x-6%2F5%29
f%28x%29=%28x%5E2-%285i%29%5E2%29%28x-6%2F5%29
f%28x%29=%28x%5E2-25%28i%29%5E2%29%28x-6%2F5%29
f%28x%29=%28x%5E2-25%28-1%29%29%28x-6%2F5%29
f%28x%29=%28x%5E2%2B25%29%28x-6%2F5%29
f%28x%29=x%5E3-%286%2F5%29x%5E2%2B25x-25%286%2F5%29
f%28x%29=x%5E3-%286%2F5%29x%5E2%2B25x-30