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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):
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