Quadratic formula and discriminant

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What is the discriminant of a quadratic equation?

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What does a positive discriminant indicate about the solutions of a quadratic equation?

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A positive discriminant indicates that the quadratic equation has two distinct real solutions.

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What does a negative discriminant indicate about the solutions of a quadratic equation?

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A negative discriminant indicates that the quadratic equation has no real solutions, but two complex solutions.

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What does a discriminant of zero indicate about the solutions of a quadratic equation?

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A discriminant of zero indicates that the quadratic equation has exactly one real solution, also known as a repeated or double root.

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What is the formula for the discriminant of a quadratic equation?

Back

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How can you determine the number of real solutions from the discriminant?

Back

If the discriminant is positive, there are two real solutions; if it is zero, there is one real solution; if it is negative, there are no real solutions.

Front

What is the quadratic formula?

Back

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The discriminant is 64.

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The discriminant is 0, indicating that there is one real solution.

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What does the discriminant tell us about the nature of the roots of a quadratic function?

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The discriminant tells us the number and type of solutions (real or complex) of the quadratic function.