SOLUTION: What is the equation of the polynomial with a leading coefficient of 2, and with the roots: -6 6 and 2i?

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Question 1010025: What is the equation of the polynomial with a leading coefficient of 2, and with the roots: -6 6 and 2i?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

the polynomial with a leading coefficient of 2, and with the roots:
x%5B1%5D=+-6
x%5B2%5D=++6+
and
x%5B3%5D=+2i-> if we have this root, we have x%5B4%5D=+-2i because complex roots always come in pairs
use zero product theorem and a leading coefficient of 2:
f%28x%29=2%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29%28x-x%5B4%5D%29
f%28x%29=2%28x-%28-6%29%29%28x-6%29%28x-2i%29%28x-%28-2i%29%29
f%28x%29=2%28x%2B6%29%28x-6%29%28x-2i%29%28x%2B2i%29
f%28x%29=2%28x%5E2-6%5E2%29%28x%5E2-%282i%29%5E2%29
f%28x%29=2%28x%5E2-36%29%28x%5E2-4i%5E2%29
f%28x%29=2%28x%5E2-36%29%28x%5E2-4%28-1%29%29
f%28x%29=2%28x%5E2-36%29%28x%5E2%2B4%29
f%28x%29=2%28x%5E4-32x%5E2-144%29
f%28x%29=2x%5E4-64x%5E2-288