SOLUTION: Find the roots of each equation using the Quadratic Formula

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Question 474706: Find the roots of each equation using the Quadratic Formula

Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
1.) x%5E2%2B2x-24=0
%28x%2B6%29%28x-4%29=0
x=4+or+-6
2.) 4x%2B32=x%5E2
x2-4x-32=0
%28x-8%29%28x%2B4%29=0
x=-4+or+8
3.) x%5E2-11x%2B30=0
%28x-5%29%28x-6%29=0
x=5+or+6..
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B2x%2B-24+=+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=%282%29%5E2-4%2A1%2A-24=100.

Discriminant d=100 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+100+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+100+%29%29%2F2%5C1+=+4
x%5B2%5D+=+%28-%282%29-sqrt%28+100+%29%29%2F2%5C1+=+-6

Quadratic expression 1x%5E2%2B2x%2B-24 can be factored:
1x%5E2%2B2x%2B-24+=+1%28x-4%29%2A%28x--6%29
Again, the answer is: 4, -6. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-24+%29

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-4x%2B-32+=+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=%28-4%29%5E2-4%2A1%2A-32=144.

Discriminant d=144 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+144+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+144+%29%29%2F2%5C1+=+8
x%5B2%5D+=+%28-%28-4%29-sqrt%28+144+%29%29%2F2%5C1+=+-4

Quadratic expression 1x%5E2%2B-4x%2B-32 can be factored:
1x%5E2%2B-4x%2B-32+=+1%28x-8%29%2A%28x--4%29
Again, the answer is: 8, -4. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-4%2Ax%2B-32+%29

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-11x%2B30+=+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=%28-11%29%5E2-4%2A1%2A30=1.

Discriminant d=1 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--11%2B-sqrt%28+1+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-11%29%2Bsqrt%28+1+%29%29%2F2%5C1+=+6
x%5B2%5D+=+%28-%28-11%29-sqrt%28+1+%29%29%2F2%5C1+=+5

Quadratic expression 1x%5E2%2B-11x%2B30 can be factored:
1x%5E2%2B-11x%2B30+=+1%28x-6%29%2A%28x-5%29
Again, the answer is: 6, 5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-11%2Ax%2B30+%29
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