The quadratic equation (k+1)x^2 + (5k-3)x+3k=0 has equal roots. Find the possible values of k.

First I would ask the student what their approach to the question would be. Most students at an A-Level standard would be aware that all quadratic equations have solutions which can be derived via the quadratic formula, this is a good place to start. From there I would try to highlight specific details of the question. For example, in this question it says equal roots. This implies that the quadratic equation has only one point where it intersects the x-axis (i.e where y=0). From further examination of the quadratic formula, it clearly has a plus/minus sign in the discriminant of the formula, which implies there would be 2 answers unless this value (discriminant) is zero. You would then plug in the values for a,b and c into the discriminant, and then simply solve for k. Be careful to fully read the question as it wants you to find ALL possible values of k, suggesting more than 1 answer is required.(in the interview I will write out some of the formula stated in this answer)