SOLUTION: third degree, only real coefficients, −2 and 2+i are two of the zeros, y-intercept is −20.

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Question 1138496: third degree, only real coefficients, −2 and 2+i are two of the zeros, y-intercept is −20.
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
the third zero is 2-i, since complex roots are conjugate.
(x+2)(x-2-i)(x-2+i) are factors
multiply the second and third.
x^2-2x+ix. -2x+4-2i. -ix+2i-i^2
This is x^2-4x+5, remembering that i^2 is -1, so that -i^2=+1
the polynomial is x^3+2x^2-4x^2-8x+5x+10=x^3-2x^2-3x+10
a(x^3-2x^2-3x+10) has to give a y-intercept of -20
so a is -2
-2x^3+4x^2+6x-20 is the polynomial.
graph%28300%2C300%2C-10%2C10%2C-30%2C30%2C-2x%5E3%2B4x%5E2%2B6x-20%29