The discriminate determines how many roots the quadratic contains. The formula is: d=b²-4ac, where a, b, and c are derived from ax²+bx+c=0. When solving for the discriminate, the properties consist of:
If d>0, the the quadratic has 2 real solutions
If d=0, the quadratic has one (repeated) solution
If d<0, the quadratic has no real roots.
You must plug d in for these inequalities to determine which one is true, and that will tell you how many solutions a quadratic contains.