SOLUTION: Find a polynomial with real coefficients of degree 3 and roots (3,2i,-2i) and that has factors :, (x-3), (x-2i) and (x+2i)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find a polynomial with real coefficients of degree 3 and roots (3,2i,-2i) and that has factors :, (x-3), (x-2i) and (x+2i)      Log On


   

Question 745584: Find a polynomial with real coefficients of degree 3 and roots (3,2i,-2i) and that has factors :, (x-3), (x-2i) and (x+2i)
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
(x-3), (x-2i) and (x+2i) tells us...
p=a%28x-3%29%28x-2i%29%28x%2B2i%29
for some constant a

%28x-2i%29%28x%2B2i%29
...is a difference of squares - with a twist:

%28x-2i%29%28x%2B2i%29=x%5E2%2B4

so we now use distribution...
p=a%28x-3%29%28x%5E2%2B4%29=a%28x%28x%5E2%2B4%29-3%28x%5E2%2B4%29%29

p=a%28x%5E3%2B4x-3x%5E2-12%29%29


p=a%28x%5E3-3x%5E2%2B4x-12%29%29
with the principal polynomial
x%5E3-3x%5E2%2B4x-12