SOLUTION: Consider the quadratic equation x^2 + px + q = 0 where p · q ≠ 0. If one root is three times the other root, find p^2/q.

Algebra ->  Finance -> SOLUTION: Consider the quadratic equation x^2 + px + q = 0 where p · q ≠ 0. If one root is three times the other root, find p^2/q.      Log On


   

Question 1150725: Consider the quadratic equation x^2 + px + q = 0 where p · q ≠ 0. If one root is three times the other root, find p^2/q.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Let the two roots be a and 3a. The sum of the roots is 4a, and their product is 3a^2.

By Vieta's Theorem, the quadratic is

x%5E2-4ax%2B3a%5E2

Then

p%5E2%2Fq+=+%28-4a%29%5E2%2F%283a%5E2%29+=+16%2F3

ANSWER: p^2/q = 16/3