SOLUTION: Find the polynomial with leading coefficient -2 that has degree 3 and roots 2 and 3i..

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Question 983477: Find the polynomial with leading coefficient -2 that has degree 3 and roots 2 and 3i..
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
the polynomial with leading coefficient -2 that has degree 3 and roots x%5B1%5D=2 and x%5B2%5D=3i
if the polynomial has x%5B2%5D=3i, then must have x%5B3%5D=-3i because complex roots always come in pairs
use zero product formula:
f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29....since given that leading coefficient is -2, multiply product above by ....substitute given roots
f%28x%29=-2%28%28x-2%29%28x-3i%29%28x-%28-3i%29%29%29
f%28x%29=-2%28%28x-2%29%28x-3i%29%28x%2B3i%29%29
f%28x%29=-2%28%28x-2%29%28x%5E2-%283i%29%5E2%29%29
f%28x%29=-2%28%28x-2%29%28x%5E2-9%28-1%29%29%29
f%28x%29=-2%28%28x-2%29%28x%5E2%2B9%29%29
f%28x%29=-2%28x%5E3%2B9x-2x%5E2-18%29
f%28x%29=-2x%5E3-18x%2B4x%5E2%2B36
f%28x%29=-2x%5E3%2B4x%5E2-18x%2B36