SOLUTION: solve by using quadratic formula 5.2x^2+5x-3=0 6.5x^2+3x-2=0 7.b^2-4ac is called the _____

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Question 539616: solve by using quadratic formula
5.2x^2+5x-3=0
6.5x^2+3x-2=0
7.b^2-4ac is called the _____
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E2%2B5x-3=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B5x%2B-3+=+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=%285%29%5E2-4%2A2%2A-3=49.

Discriminant d=49 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+49+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%285%29%2Bsqrt%28+49+%29%29%2F2%5C2+=+0.5
x%5B2%5D+=+%28-%285%29-sqrt%28+49+%29%29%2F2%5C2+=+-3

Quadratic expression 2x%5E2%2B5x%2B-3 can be factored:
2x%5E2%2B5x%2B-3+=+2%28x-0.5%29%2A%28x--3%29
Again, the answer is: 0.5, -3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B5%2Ax%2B-3+%29

.
5x%5E2%2B3x-2=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B3x%2B-2+=+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=%283%29%5E2-4%2A5%2A-2=49.

Discriminant d=49 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+49+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+49+%29%29%2F2%5C5+=+0.4
x%5B2%5D+=+%28-%283%29-sqrt%28+49+%29%29%2F2%5C5+=+-1

Quadratic expression 5x%5E2%2B3x%2B-2 can be factored:
5x%5E2%2B3x%2B-2+=+5%28x-0.4%29%2A%28x--1%29
Again, the answer is: 0.4, -1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B3%2Ax%2B-2+%29

.
b%5E2-4ac is called the discriminant.