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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 From this formula the discriminant is: b 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. |