SOLUTION: Determine a polynomial P(x) with real coefficients and of degree 5 for which three of its roots are x = -1, x = 1 + 2i and x = -3i.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Determine a polynomial P(x) with real coefficients and of degree 5 for which three of its roots are x = -1, x = 1 + 2i and x = -3i.      Log On


   

Question 905134: Determine a polynomial P(x) with real coefficients and of degree 5 for which three of its roots are x = -1, x = 1 + 2i and x = -3i.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Since the coefficients are real, the complex roots come in complex conjugate pairs.
P%28x%29=%28x%2B1%29%28x-%281%2B2i%29%29%28x-%281-2i%29%29%28x%2B3i%29%28x-3i%29
P%28x%29=%28x%2B1%29%28x%5E2-2x%2B5%29+%28x%5E2%2B9%29
P%28x%29=%28x%5E3-x%5E2%2B3x%2B5%29%28x%5E2%2B9%29
P%28x%29=x%5E5-x%5E4%2B12x%5E3-4x%5E2%2B27x%2B45