SOLUTION: What is the solution set of the equation {{{ x^2 - 5x -24 = 0 }}}

Algebra ->  Expressions -> SOLUTION: What is the solution set of the equation {{{ x^2 - 5x -24 = 0 }}}      Log On


   

Question 695267: What is the solution set of the equation +x%5E2+-+5x+-24+=+0+
Answer by mouk(232) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-5x%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=%28-5%29%5E2-4%2A1%2A-24=121.

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

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+121+%29%29%2F2%5C1+=+8
x%5B2%5D+=+%28-%28-5%29-sqrt%28+121+%29%29%2F2%5C1+=+-3

Quadratic expression 1x%5E2%2B-5x%2B-24 can be factored:
1x%5E2%2B-5x%2B-24+=+1%28x-8%29%2A%28x--3%29
Again, the answer is: 8, -3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-5%2Ax%2B-24+%29