Find the values of k ε R subject to the following condition :
The ratio of the rots of $x^2 + 3kx + 20 = 0$ is 4 : 5.
If $x^2 - 6x + α = 0 has two roots α, β and 3α + 2β = 20, then find a.
If the roots of the equations $x^2 + 3kx + 2 = 0$ are in the ratio of 1 : 2, then find the value of k.
If the difference of the roots of the equation $x^2 - 2kx + 3k = 0$ is 4, then find the value of k.
The quadratic equation whose roots are twice the roots of $2x^2 - 5x + 2 = 0$ is :