SOLUTION: Given that the roots of x^2+px+q=0 are (alpha) and 4(alpha) show that 4p^2= 25q.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Given that the roots of x^2+px+q=0 are (alpha) and 4(alpha) show that 4p^2= 25q.      Log On


   

Question 173792: Given that the roots of x^2+px+q=0 are (alpha) and 4(alpha) show that 4p^2= 25q.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
The roots of x%5E2%2Bpx%2Bq=0 are alpha and 4alpha if and only if %28x-alpha%29 and %28x-4alpha%29 are factors of x%5E2%2Bpx%2Bq. So:



Hence: p=-5alpha and q=4alpha%5E2

4p%5E2=4%28-5alpha%29%5E2=4%2A25alpha%5E2=100alpha%5E2

25q=25%2A4alpha%5E2=100alpha%5E2

QED