1. The problem statement, all variables and given/known data The real values of a for which the equation x^2-3x+a=0 has three real and distinct roots is 3. The attempt at a solution I started by writing the sign scheme of f'(x). But it is of no help to me. It will merely tell me the intervals in which f(x) increases or decreases. Also, if there are three distinct roots of f(x) then there must be two extrema.