SOLUTION: Find a polynomial p of degree 3 such that −2, −1, and 4 are zeros of p and p(1) = 2

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Question 974211: Find a polynomial p of degree 3 such that −2, −1, and 4 are zeros of p and
p(1) = 2
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
a(x^3+x^2+x+d)=0
factors are inverses of roots
(x+2)(x+1)(x-4)
Multiply them:
first two are x^2+3x+2
multiply by (x-4)
x^3-4x^2+3x^2-12x+2x-8
=x^3-x^2-10x-8, the general form of the polynomial
a(x^3-x^2-10x-8)=2, when x=1
a(1-1-10-8)=2
-18a=2
a=-1/9
polynomial is (-1/9)(x^3-x^2-10x-8)



graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C%28-1%2F9%29%28x%5E3-x%5E2-10x-8%29%29