Finding values for K such that the roots of the quadratic are strictly imaginary: $x^2+\left(K^2+3K-7\right)x+K$ $x^2+\left(K^2+3K-7\right)x+K$ 
I'd like to know the general approach needed to find out how to find solutions for K when I want the roots of this equation to have a specific property, such as strictly imaginary, or when I want them to have a positive real part only, or negative real part only.
Bonus points if the approach applies to a general quadratic of the form $ax^2+bx+c$, what equations should be satisfied if I want specific properties for the roots? Extra bonus points for the same question, but for cubic and quartic equations.

The real part comes from coefficient of $x$, so this coefficient should be $0$ or
$$K^2+3K-7=0$$
then solve it and check if the $K>0$ to get what you need 
