SOLUTION: Find the zero of the function. Give approximate solutions rounded to three decimal place when necessary. f(x)=5x^2+6x-7 the answer is -1.927, 0.727

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Question 922463: Find the zero of the function. Give approximate solutions rounded to three decimal place when necessary.
f(x)=5x^2+6x-7
the answer is -1.927, 0.727
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B6x%2B-7+=+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=%286%29%5E2-4%2A5%2A-7=176.

Discriminant d=176 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+176+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%286%29%2Bsqrt%28+176+%29%29%2F2%5C5+=+0.72664991614216
x%5B2%5D+=+%28-%286%29-sqrt%28+176+%29%29%2F2%5C5+=+-1.92664991614216

Quadratic expression 5x%5E2%2B6x%2B-7 can be factored:
5x%5E2%2B6x%2B-7+=+5%28x-0.72664991614216%29%2A%28x--1.92664991614216%29
Again, the answer is: 0.72664991614216, -1.92664991614216. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B6%2Ax%2B-7+%29