1. The problem statement, all variables and given/known data Find all real numbers k such that x^2+kx+k is reducible in ℝ[x]. 2. Relevant equations 3. The attempt at a solution This seems like it is simple, but it is new to me so I am looking for confirmation. We know we can find the roots of a polynomial with b^2-4ab. We want b^2-4ab to be greater than 0 for it to have roots. But we note: Here, a = 1, b = b, c = b. When we have b^2-4*b = 0 we get the answers either b = 0 or b = 4. Both of these are solutions to the problem question. If we let b(b-4) > 0 then we get a whole array of numbers that are not solutions to this problem. So I am stating that b =0 and b = 4 are the only solutions to the problem as they are the only solutions to b^2-4ab = 0. But why is this so?