
Using the Discriminant to predict the roots of a quadratic equationThe discriminant of a quadratic equation is the value under the square root sign in the quadratic formula. Remember the quadratic formula for an equation in the form ax + bx + c = 0 is: From this formula the discriminant is: b  4ac When you evaluate the discriminant for a quadratic equation, if the result is:
Examples: Use the discriminant to predict the roots of the following equations:
Since the result is positive, there should be 2 different real solutions. In fact, there will be 2 different rational solutions because 1 is a perfect square number. (Perfect square numbers are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, etc)
Since the result is positive, there should be 2 different real solutions. In fact, there will be 2 different irrational solutions because 37 is not a perfect square number.
Since the result is zero, there should be only one real, rational solution
Since the result is negative, there should be no real solutions. 