SOLUTION: Use the quadratic formula to find the zeros of f. f(x)= -12x^2+11x+15

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Question 1050590: Use the quadratic formula to find the zeros of f.
f(x)= -12x^2+11x+15
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Use the quadratic formula to find the zeros of f.
f(x)= -12x^2+11x+15
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Do it like this one:
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -3x%5E2%2B7x%2B11+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%287%29%5E2-4%2A-3%2A11=181.

Discriminant d=181 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-7%2B-sqrt%28+181+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%287%29%2Bsqrt%28+181+%29%29%2F2%5C-3+=+-1.07560400784562
x%5B2%5D+=+%28-%287%29-sqrt%28+181+%29%29%2F2%5C-3+=+3.40893734117895

Quadratic expression -3x%5E2%2B7x%2B11 can be factored:
-3x%5E2%2B7x%2B11+=+%28x--1.07560400784562%29%2A%28x-3.40893734117895%29
Again, the answer is: -1.07560400784562, 3.40893734117895. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-3%2Ax%5E2%2B7%2Ax%2B11+%29