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If the discriminant is positive--if b2 -4ac > 0--then the quadratic equation has two solutions.
If the discriminant is zero--if b2 - 4ac = 0--then the quadratic equation has one solution.
If the discriminant is negative--if b2 -4ac < 0--then the quadratic equation has no solutions.
Example: How many solutions does the quadratic equation 2x2 + 5x + 2 have?
a = 2, b = 5, and c = 2.
b2 -4ac = 52 -4(2)(2) = 25 - 16 = 9 > 0.
Thus, the quadratic equation has 2 solutions.
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