Question 6931
 This means: If you had a polynomial (say, in x) and you solved it to find its roots and they turned out to be: x = -1/2 and x = 2/3, what would that polynomial look like?

Well, first, since there are two roots, the polynomial must be a quadratic function like: f(x) = ax^2 + bx + c

Now, if you have the roots to a quadratic function, you can form the factors of that function by recalling how you get the roots to a quadratic function in the first place.

If the roots are x = -1/2 and x = 2/3 then the factors would be:

(2x + 1) and (3x - 2) 

Why is this? 

Because to get the roots of the quadratic, you had to set each of the factors equal to zero, as in: (2x + 1) = 0, so x = -1/2 and (3x - 2) = 0, so x = 2/3

Now you have the factors of the quadratic function, you can find the function itself by multiplying these factors, (x + 1/2)(x - 2/3).

If you do this, you will get: 

{{{f(x) = 6x^2 - x - 2}}}

Check, using FOIL:

{{{(2x + 1)(3x - 2) = 6x^2 - 4x + 3x - 2 = 6x^2 - x - 2}}}