Question 579188: I'm working on factoring trinomials, and I cannot find the answer to two problems.
1. x squared -4x+24
2. k squared -13k+40
Answer by dfrazzetto(283)   (Show Source):
You can put this solution on YOUR website! 1. x squared -4x+24
x^2 -4x + 24
Cannot be factored, (non-integer roots), verify w/ quadratic equation
| Solved by pluggable solver: SOLVE quadratic equation with variable |
Quadratic equation  (in our case  ) has the following solutons:
For these solutions to exist, the discriminant  should not be a negative number.
First, we need to compute the discriminant :  .
The discriminant -80 is less than zero. That means that there are no solutions among real numbers.
If you are a student of advanced school algebra and are aware about imaginary numbers, read on.
In the field of imaginary numbers, the square root of -80 is + or -  .
The solution is 
Here's your graph:
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2. k squared -13k+40
Can be factored:
(k-5)(k-8) = k^2 -13k + 40 √
| Solved by pluggable solver: SOLVE quadratic equation with variable |
Quadratic equation  (in our case  ) has the following solutons:
For these solutions to exist, the discriminant should not be a negative number.
First, we need to compute the discriminant :  .
Discriminant d=9 is greater than zero. That means that there are two solutions:  .
Quadratic expression  can be factored:
Again, the answer is: 8, 5.
Here's your graph:
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