The equation x^2 + 3px + p = 0, where p is a non-zero constant, has equal roots. Find the value of p.

Firstly, we need to recognise that the question stated that the quadratic equation has equal roots. This tells us that the discriminant of the equation (b^2 - 4ac) will be an important part of the solution. If we model the equation given in the form ax^2 + bx + c, we would know that in this case, a = 1, b = 3p and c = p. If a quadratic equation has equal roots, we know that b^2 – 4ac = 0. Substituting the values for a, b, and c in, we get another quadratic equation in terms of p: 9p^2 - 4p = 0. We can factorise out p to get p(9p - 4) = 0, which gives us the solutions p = 0 and p = 4/9. Going back to the question, we’re told that p is a non-zero constant, which means that we can eliminate p = 0 as a solution. This leaves us with p = 4/9.