SOLUTION: Find an equation that has the given solutions: X=-2i and X=-3i How do I proceed?

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Find an equation that has the given solutions: X=-2i and X=-3i How do I proceed?      Log On


   

Question 313486: Find an equation that has the given solutions:
X=-2i and X=-3i
How do I proceed?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Complex roots only come in complex conjugate pairs.
So if x=-2i is a root so is x=2i.
Same for x=-3i.
So the equation looks like,
f%28x%29=A%28x-2i%29%28x%2B2i%29%28x-3i%29%28x%2B3i%29 where A is any non-zero constant.
f%28x%29=A%28x%5E2%2B2ix-2ix-4i%5E2%29%28x%5E2%2B3ix-3ix-9i%5E2%29
f%28x%29=A%28x%5E2%2B4%29%28x%5E2%2B9%29
f%28x%29=A%28%28x%5E2%2B4%29x%5E2%2B%28x%5E2%2B4%299%29
f%28x%29=A%28%28x%5E4%2B4x%5E2%29%2B%289x%5E2%2B36%29%29
f%28x%29=A%28x%5E4%2B13x%5E2%2B36%29