How do you write a polynomial when given three roots?
r1 = root 1 ---> x - r1 = 0
r2 = root 2 ----> x - r2 = 0
r3 = root 3 ----> x - r3 = 0
you just line them up and distribute
(x - r1)(x - r2)(x - r3) = 0
and you end up with
x3 - (r1 + r2 + r3)x2 + (r1r2 + r1r3 + r2r3)x - (r1*r2*r3) = 0
Remember that the roots satisfy f(x)=0. Some time ago you solved polynomials by factoring, and used the zero-product property to find the roots. For example, suppose you factored x2-4x-5=0 and got (x+1)(x-5)=0. By the zero-product property, your roots are -1 and 5.
Going from the roots to the polynomial is like going backwards. Suppose you are given -2, 3, and 0 as roots. You could write it in the factored form:
(You can check by plugging in the roots and seeing that the result=0.)
Now to find the polynomial, multiply the terms.
x(x+2)(x-3) = (x2+2x)(x-3) = x3-3x2+2x2-6x = x3-x2-6x
So in my sample, x3-x2-6x is the polynomial with roots -2, 0, and 3
I hope this answers your question! Let me know if you need clarification.