Expert: Steve Holleran - 12/31/2007

Question
x^2-2kx+12=0 has two positive roots, one which is three times the other. What is k and what are the roots?

Answer
Hello Nivedha,

I used some facts about quadratics that are sometimes forgotten to do this:

For a quadratic in the form ax^2 + bx + c = 0, the sum of the roots is -b/a and the product of the roots is c/a.

Here, a = 1, b = -2k, and c = 12.

So if we call the roots r1 = r and r2 = 3r, we have :

Sum :   r + 3r = -(-2k/1) --> 4r = 2k  --> k = 2r

Product:  r * 3r = 3r^2 = 12/1

so                 3r^2 = 12 --> r^2 = 4 --> r=2 since the roots are positive.  The other root is then 3r = 3 * 2 = 6 and  k = 2r = 2(2) = 4.


Hope this is okay to understand.

Steve