SOLUTION: if (p+3) and (q-4) are the roots of the equation x^2=8x-15. What is the values of p and q?

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: if (p+3) and (q-4) are the roots of the equation x^2=8x-15. What is the values of p and q?       Log On


   

Question 564109: if (p+3) and (q-4) are the roots of the equation x^2=8x-15. What is the values of p and q?

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Let's write that equation in a more conventional form.
x%5E2=8x-15 ---> x%5E2-8x%2B15=0
If you are good at factoring you immediately realize that
x%5E2-8x%2B15=%28x-5%29%28x-3%29
which means that the equation can be written as
%28x-5%29%28x-3%29=0
showing that the solutions are x=5 and x=3 .
If you do not like factoring, you would solve the equation in a different way (maybe apply the quadratic formula or complete the square).
No matter how you solve the equation, the solutions are x=5 and x=3 .
But which one is (p+3) and which one is (q-4)? No way to tell.
There will be two solution sets:
If p+3=5 and q-4=3, p=2 and q=7.
If p+3=3 and q-4=5, p=0 and q=9.