SOLUTION: {{{z^2-13z+36=0}}}

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: {{{z^2-13z+36=0}}}      Log On


   

Question 18987: z%5E2-13z%2B36=0
Answer by Alwayscheerful(414) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation az%5E2%2Bbz%2Bc=0 (in our case 1z%5E2%2B-13z%2B36+=+0) has the following solutons:

z%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=%28-13%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.

z%5B1%5D+=+%28-%28-13%29%2Bsqrt%28+25+%29%29%2F2%5C1+=+9
z%5B2%5D+=+%28-%28-13%29-sqrt%28+25+%29%29%2F2%5C1+=+4

Quadratic expression 1z%5E2%2B-13z%2B36 can be factored:
1z%5E2%2B-13z%2B36+=+1%28z-9%29%2A%28z-4%29
Again, the answer is: 9, 4. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-13%2Ax%2B36+%29

Hope this helps!