SOLUTION: 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

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:

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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