2-6 The Discriminant

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What is the discriminant of a quadratic equation?

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What does a discriminant of 0 indicate about the solutions of a quadratic equation?

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A discriminant of 0 indicates that the quadratic equation has exactly one real solution, also known as a double root.

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If the discriminant is positive, how many real solutions does the quadratic equation have?

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If the discriminant is positive, 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 (imaginary) solutions.

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How can you determine the nature of the roots of a quadratic equation using the discriminant?

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You can determine the nature of the roots by evaluating the discriminant: if > 0, two real solutions; if = 0, one real solution; if < 0, no real solutions.

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What is the formula for finding the zeros of a quadratic equation?

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If a quadratic equation has a discriminant of 25, what can you say about its solutions?

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Since the discriminant is positive (25), the quadratic equation has two distinct real solutions.