SOLUTION: write a polynomial of the 5th degree that has the given numbers as its zeros: -2, -1, 0, -2i. multiply all factors out, do not leave in factored form.

Question 55205: write a polynomial of the 5th degree that has the given numbers as its zeros: -2, -1, 0, -2i. multiply all factors out, do not leave in factored form.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
write a polynomial of the 5th degree that has the given numbers as its zeros: -2, -1, 0, -2i. multiply all factors out, do not leave in factored form.
:
How about this?
mult x*(x+2)*(x+1)= x^3 + 3x^2 + 2x
:
x = -2i
Square both sides:
x^2 = 4(-1)
x^2 = -4
x^2 + 4 = 0
:
(x^2 + 4)*(x^3 + 3x^2 + 2x) = x^5 + 3x^4 + 6x^3 + 12x^2 + 8x
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