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.