SOLUTION: Given one roots of x^2+px+8=0 is two times of the other. Find the roots and p.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Given one roots of x^2+px+8=0 is two times of the other. Find the roots and p.      Log On


   

Question 408299: Given one roots of x^2+px+8=0 is two times of the other. Find the roots and p.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Interesting thing about this problem is that the roots and the value of p are not uniquely determined. You'll see why:

Suppose the two roots are r and 2r. The product of the roots is 8 by Vieta's formulas, so 2r%5E2+=+8 --> r%5E2+=+4 --> r = +/- 2. Hence, the roots are {2, 4} or {-2, -4}. Also, the sum of the roots is -p, so p = -6 or 6, respectively.

Hence, the quadratic x%5E2+-+6x+%2B+8 has roots {2, 4} and x%5E2+%2B+6x+%2B+8 has roots {-2, -4}.