SOLUTION: How do you factor 21x^2-59x+40?

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Question 534357: How do you factor 21x^2-59x+40?
Answer by Maths68(1474) About Me  (Show Source):
You can put this solution on YOUR website!
=21x^2-59x+40?
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 21x%5E2%2B-59x%2B40+=+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=%28-59%29%5E2-4%2A21%2A40=121.

Discriminant d=121 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--59%2B-sqrt%28+121+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-59%29%2Bsqrt%28+121+%29%29%2F2%5C21+=+1.66666666666667
x%5B2%5D+=+%28-%28-59%29-sqrt%28+121+%29%29%2F2%5C21+=+1.14285714285714

Quadratic expression 21x%5E2%2B-59x%2B40 can be factored:
21x%5E2%2B-59x%2B40+=+21%28x-1.66666666666667%29%2A%28x-1.14285714285714%29
Again, the answer is: 1.66666666666667, 1.14285714285714. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+21%2Ax%5E2%2B-59%2Ax%2B40+%29