SOLUTION: Factoring Completely: How could you factor a problem like this: (a^2

Question 159228: Factoring Completely: How could you factor a problem like this: (a^2 - 10ab + 3b^2)
Answer by Alan3354(21581) (Show Source):
You can put this solution on YOUR website!
Factoring Completely: How could you factor a problem like this: (a^2 - 10ab + 3b^2)
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The factors will have the form (a - Rb)*(a - Sb) where R and S are to be found.
R*S = +3 and R+S = -10. R and S have to be negative, since their sum is negative and their product is positive.
There are no integers that fit.
The values can be found by using the quadratic eqn:

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

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=88 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 9.69041575982343, 0.30958424017657. Here's your graph:

The values are R = (5 + sqrt(22)) and S = (5 - sqrt(22))
Sub those for R and S into (a - Rb)*(a - Sb)

SOLUTION: Factoring Completely: How could you factor a problem like this: (a^2 - 10ab + 3b^2)