SOLUTION: USE QUADRATIC FORMULA FOR 4X^2=3

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: USE QUADRATIC FORMULA FOR 4X^2=3      Log On


   

Question 467792: USE QUADRATIC FORMULA FOR
4X^2=3
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
4x2-3=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B0x%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=%280%29%5E2-4%2A4%2A-3=48.

Discriminant d=48 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-0%2B-sqrt%28+48+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%280%29%2Bsqrt%28+48+%29%29%2F2%5C4+=+0.866025403784439
x%5B2%5D+=+%28-%280%29-sqrt%28+48+%29%29%2F2%5C4+=+-0.866025403784439

Quadratic expression 4x%5E2%2B0x%2B-3 can be factored:
4x%5E2%2B0x%2B-3+=+4%28x-0.866025403784439%29%2A%28x--0.866025403784439%29
Again, the answer is: 0.866025403784439, -0.866025403784439. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B0%2Ax%2B-3+%29