SOLUTION: please help, -number of real solutions- 1.) -3x^2+9x-8=0 2.)8x^2-11x=-3 3.)x^2=-7x+7 4.)-4x^2-4=8x i have a test in ALG2 today please quick response thank you

Algebra ->  Real-numbers -> SOLUTION: please help, -number of real solutions- 1.) -3x^2+9x-8=0 2.)8x^2-11x=-3 3.)x^2=-7x+7 4.)-4x^2-4=8x i have a test in ALG2 today please quick response thank you      Log On


   

Question 547116: please help,
-number of real solutions-
1.) -3x^2+9x-8=0
2.)8x^2-11x=-3
3.)x^2=-7x+7
4.)-4x^2-4=8x
i have a test in ALG2 today please quick response thank you
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
1)-3x%5E2%2B9x-8=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -3x%5E2%2B9x%2B-8+=+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=%289%29%5E2-4%2A-3%2A-8=-15.

The discriminant -15 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -15 is + or - sqrt%28+15%29+=+3.87298334620742.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-3%2Ax%5E2%2B9%2Ax%2B-8+%29
no real number answers
2)8x%5E2-11x%2B3=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 8x%5E2%2B-11x%2B3+=+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%2A8%2A3=25.

Discriminant d=25 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--11%2B-sqrt%28+25+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-11%29%2Bsqrt%28+25+%29%29%2F2%5C8+=+1
x%5B2%5D+=+%28-%28-11%29-sqrt%28+25+%29%29%2F2%5C8+=+0.375

Quadratic expression 8x%5E2%2B-11x%2B3 can be factored:
8x%5E2%2B-11x%2B3+=+8%28x-1%29%2A%28x-0.375%29
Again, the answer is: 1, 0.375. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+8%2Ax%5E2%2B-11%2Ax%2B3+%29
2 answers
3)x%5E2%2B7x-7=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B7x%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=%287%29%5E2-4%2A1%2A-7=77.

Discriminant d=77 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-7%2B-sqrt%28+77+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%287%29%2Bsqrt%28+77+%29%29%2F2%5C1+=+0.887482193696061
x%5B2%5D+=+%28-%287%29-sqrt%28+77+%29%29%2F2%5C1+=+-7.88748219369606

Quadratic expression 1x%5E2%2B7x%2B-7 can be factored:
1x%5E2%2B7x%2B-7+=+1%28x-0.887482193696061%29%2A%28x--7.88748219369606%29
Again, the answer is: 0.887482193696061, -7.88748219369606. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B7%2Ax%2B-7+%29
2 answers
4)-4x%5E2-8x-4=0
-4%28x%5E2%2B2x%2B1%29=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B2x%2B1+=+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%2A1=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%282%29%29%2F2%5C1.
Expression can be factored: 1x%5E2%2B2x%2B1+=+1%28x--1%29%2A%28x--1%29

Again, the answer is: -1, -1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B1+%29
2 answers