Expert: Steve Holleran - 5/27/2007

Question
If x^2 + px + q = 0, what is (p^2)/q if one root is five times the other?

Answer
Hello Austin,

To do this, I made use of a couple of obscure results about quadratic equations:

For any quadratic of the form ax^2 + bx + c = 0,

I.  The sum of the roots is -b / a.

II. The product of the roots is c / a.

Here we have a = 1, b = p , c = q, so if we call the roots
k and 5k, then:

  k + 5k = -p / 1 ---> 6k = -p --> p = 6k --> p^2 = 36k^2

  k * 5k = q / 1 -----> 5k^2 = q

So then p^2 / q = 36k^2 / 5k^2 = 36 / 5 = 7.2

I hope this is what you needed.

Steve Holleran