SOLUTION: directions: write the polynomial function having given the roots. (i don't know what this means.) -1/2,2/3 (its shown as fractions) thank you.

Question 6931: directions: write the polynomial function having given the roots.
(i don't know what this means.)
-1/2,2/3 (its shown as fractions)
thank you.
Found 2 solutions by Earlsdon, glabow:
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
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:

Check, using FOIL:

Answer by glabow(165) (Show Source): You can put this solution on YOUR website!
The roots of a function are those values of x for which the function evaluates to 0. That is, when a function is of the form

a zero is a value for x that makes y = 0.
Since many functions can be factored, you begin by writing the known roots as factors of y. Your values would be

When the first term becomes 0. In this equation, then, y = 0. When the second term becomes 0. Then y = 0.
All that is needed is to multiply out the factors.

Simplifying gives

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