SOLUTION: a2+13a+36=0

Algebra ->  Algebra  -> Linear-equations -> SOLUTION: a2+13a+36=0      Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 23452: a2+13a+36=0
Answer by stanbon(57219) About Me  (Show Source):
You can put this solution on YOUR website!
Quadratic with a=1, b=13, c=36
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aa%5E2%2Bba%2Bc=0 (in our case 1a%5E2%2B13a%2B36+=+0) has the following solutons:

a%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=%2813%29%5E2-4%2A1%2A36=25.

Discriminant d=25 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-13%2B-sqrt%28+25+%29%29%2F2%5Ca.

a%5B1%5D+=+%28-%2813%29%2Bsqrt%28+25+%29%29%2F2%5C1+=+-4
a%5B2%5D+=+%28-%2813%29-sqrt%28+25+%29%29%2F2%5C1+=+-9

Quadratic expression 1a%5E2%2B13a%2B36 can be factored:
1a%5E2%2B13a%2B36+=+1%28a--4%29%2A%28a--9%29
Again, the answer is: -4, -9. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B13%2Ax%2B36+%29


Cheers,
Stan H.