The expression b²-4acof the quadratic formula is called the discriminantof the quadratic equation ax² + bx + c = 0. This determines the nature of the roots of a quadratic equation.
If the discriminant is negative or b² - 4ac < 0, the roots are imaginary and unequal. Therefore, we can say that there are no real solutions. If a quadratic equation of such roots is graphed, there is no x-intercept, meaning the parabola will not touch the x-axis.
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✎ Nature of the Roots of a Quadratic Equation
» When b² - 4ac < 0, the are no solutions.
Explanation:
The expression b² - 4ac of the quadratic formula
is called the discriminant of the quadratic equation ax² + bx + c = 0. This determines the nature of the roots of a quadratic equation.
If the discriminant is negative or b² - 4ac < 0, the roots are imaginary and unequal. Therefore, we can say that there are no real solutions. If a quadratic equation of such roots is graphed, there is no x-intercept, meaning the parabola will not touch the x-axis.
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