SOLUTION: Find the polynomial with degree 5. Zeros -2,1,2,i. Y-int of (0,-8)

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Question 1114694: Find the polynomial with degree 5. Zeros -2,1,2,i. Y-int of (0,-8)
Answer by Boreal(15235) About Me  (Show Source):
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The factors are (x+2)(x-2)(x-1), (x-i) and (x+i), because if i is a factor, -i is also a factor
This is (x^2-4)(x-1)and (x^2+1), the latter giving rise to roots of +/- i
That is (x^4-3x^2-4)(x-1), or
x^5-x^4-3x^3+3x^2-4x+4
or a(x^5-x^4+3x^2-4x+4)=-8, when x=0
so 4a=-8 and a =-2
polynomial is -2(x^5-x^4+3x^2-4x+4) ANSWER