SOLUTION: Factor {{{30z^2-87z+30}}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Factor {{{30z^2-87z+30}}}      Log On


   

Question 312609: Factor 30z%5E2-87z%2B30
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
30z%5E2-87z%2B30
30%28z%5E2-2.9z%2B1%29
30%28z-2.5%29%28z%2B0.4%29 <---Factored
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation az%5E2%2Bbz%2Bc=0 (in our case 30z%5E2%2B-87z%2B30+=+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=%28-87%29%5E2-4%2A30%2A30=3969.

Discriminant d=3969 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--87%2B-sqrt%28+3969+%29%29%2F2%5Ca.

z%5B1%5D+=+%28-%28-87%29%2Bsqrt%28+3969+%29%29%2F2%5C30+=+2.5
z%5B2%5D+=+%28-%28-87%29-sqrt%28+3969+%29%29%2F2%5C30+=+0.4

Quadratic expression 30z%5E2%2B-87z%2B30 can be factored:
30z%5E2%2B-87z%2B30+=+30%28z-2.5%29%2A%28z-0.4%29
Again, the answer is: 2.5, 0.4. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+30%2Ax%5E2%2B-87%2Ax%2B30+%29