SOLUTION: find a degree 3 polynomial with coefficient of x^3 equal to 1 and zeros 2,-5i and 5i

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Question 781983: find a degree 3 polynomial with coefficient of x^3 equal to 1 and zeros 2,-5i and 5i
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

ax%5E3%2Bbx%5E2%2Bcx%2Bd=0 where a=1
so, your polynomial will be x%5E3%2Bbx%5E2%2Bcx%2Bd=0
use zero product rule since you are given zeros x%5B1%5D=2,x%5B2%5D=-5i and x%5B3%5D=5i
%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29=0
%28x-2%29%28x-%28-5i%29%29%28x-5i%29=0
%28x-2%29%28x%2B5i%29%28x-5i%29=0 ......%28x%2B5i%29%28x-5i%29=x%5E2-%285i%29%5E2=x%5E2-%2825%28-1%29%29=x%5E2%2B25
%28x-2%29%28x%5E2%2B25%29=0
x%5E3%2B25x-2x%5E2-50=0
x%5E3-2x%5E2%2B25x-50=0