# Math Help - Roots of a quadratic

1. ## Roots of a quadratic

Hi all,
I would appreciate some help on how to solve the following problem.

If x^2+kx+54=0 has one root that is twice the other root, what are the values of k?

Thanks a lot!

2. Originally Posted by asamimasa
Hi all,
I would appreciate some help on how to solve the following problem.

If x^2+kx+54=0 has one root that is twice the other root, what are the values of k?

Thanks a lot!
The equation has the solutions:

$x = t~\vee~ x = 2t$

Then

$(x-t)(x-2t)=0~\implies~x^2-3t+2t^2 = 0$

Thus:

$2t^2 = 54 ~\implies~t = 3\sqrt{3}~\vee~t = -3\sqrt{3}$

And therefore

$k = -9\sqrt{3}~\vee~k=9\sqrt{3}$