The nonzero roots of the equation $x^2 + 6x + k = 0$ are in the ratio $2:1$ . What is the value of $k$ ?
Let the roots be r and 2r:
(x-r)*(x-2r) = x^2 + 6x + k
x^2 - 3rx + 2r^2 = x^2 + 6x + k
-3r = 6, hence r = -2
k = 2r^2 Hence k = 8