The Discriminant

Front

What is the Discriminant in a quadratic equation?

Back

The Discriminant is a value calculated from the coefficients of a quadratic equation in the form ax² + bx + c. It is given by the formula D = b² - 4ac.

Front

What does a positive Discriminant indicate about the roots of a quadratic equation?

Back

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

Front

What does a Discriminant of zero indicate about the roots of a quadratic equation?

Back

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 does a negative Discriminant indicate about the roots of a quadratic equation?

Back

A negative Discriminant indicates that the quadratic equation has two complex (non-real) solutions.

Front

Calculate the Discriminant for the quadratic equation: 2x² + 3x + 1.

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D = b² - 4ac = 3² - 4(2)(1) = 9 - 8 = 1 (positive, so 2 distinct real solutions).

Front

Calculate the Discriminant for the quadratic equation: x² - 4x + 4.

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D = b² - 4ac = (-4)² - 4(1)(4) = 16 - 16 = 0 (one real solution).

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Calculate the Discriminant for the quadratic equation: x² + 2x + 5.

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D = b² - 4ac = 2² - 4(1)(5) = 4 - 20 = -16 (two complex solutions).

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What is the significance of the Discriminant in determining the nature of roots?

Back

The Discriminant helps determine the number and type of roots of a quadratic equation without solving it.

Front

If the Discriminant is 113, how many real solutions does the quadratic equation have?

Back

The quadratic equation has two distinct real solutions.

Front

If the Discriminant is -44, how many real solutions does the quadratic equation have?

Back

The quadratic equation has two complex solutions.