SOLUTION: Let f(x)=3x^2-8x. find a such that f(a)=-5.

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Question 240777: Let f(x)=3x^2-8x. find a such that f(a)=-5.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
If f%28x%29+=+3x%5E2-8x, then f%28a%29+=+3a%5E2+-8a. And if f(a) = -5 then -5+=+3a%5E2+-8a.

Now we just solve for a. Since this is a quadratic equation we will
1) Get one side equal to zero (by adding 5 to each side):
0+=+3a%5E2+-+8a+%2B5
2) Factor (and use the Zero Product Property) or use the Quadratic Formula.
0+=+%283a+-+5%29%28a-1%29
By the Zero Product Property, this or any product can be zero only if one (or more) of the factors is zero. So
3a+-+5+=+0 or a-1+=+0
Solving these two equations we get:
3a+=+5 or a+=+1
a+=+5%2F3 of a+=+1 (You will get these same answers if you use the Quadratic formula correctly.)