A distinct real solution is a solution to an equation that occurs once, and differs in value from other solutions. For example, in the equation above there are two distinct real solutions: x = − 13 2 and x = 13 2 . Since they are different, real numbers, the equation has two distinct real solutions.
The value of the discriminant determines how many solutions the quadratic will have. Equation 1: the discriminant was zero, there was only 1 solution. Equation 2: the discriminant was a negative number, there was no solution. Equation 3: the discriminant was a positive number, there were two solutions.
