I was going through my year 12 text book doing complex numbers when in chapter review I was faced with a question I've got no idea how to answer.
Consider the equation $x^2+4x-1+k(x^2+2x+1)=0$. Find the set of real values for $k$ where $k$ $\neq -1$ for which the two solutions of the equation are:
Real & Distinct, Real & Equal, Complex with positive real part and non-zero imaginary part
Please help me guys, there is nothing like this in the chapter questions and even my teacher is stumped as the book has the answers but no working out.