The discriminant of an equation is the expression found underneath the square root sign in the quadratic equation (b2-4ac). If this discriminant is greater than zero, there will be two solutions. The parabola will cross the x axis two times. If the discriminant equals zero, there will be only one solution. The parabola just touches the x axis one time. If the discriminant is less than zero, you will have two complex solutions, which will be conjugates of each other. The parabola never touches the x axis.
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Last updated: 01/25/2018
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