The Discriminant

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What is the Discriminant in a quadratic equation?

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The Discriminant is the part of the quadratic formula under the square root, given by the expression b² - 4ac, where a, b, and c are coefficients of the quadratic equation ax² + bx + c = 0.

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What does a Discriminant value of 0 indicate?

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A Discriminant value of 0 indicates that the quadratic equation has exactly one real solution (a repeated root).

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What does a positive Discriminant value indicate?

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

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What does a negative Discriminant value indicate?

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A negative Discriminant value 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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The Discriminant is b² - 4ac = 3² - 4(2)(1) = 9 - 8 = 1 (positive, so 2 real solutions).

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

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

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If the Discriminant is -63, how many solutions does the quadratic equation have?

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The quadratic equation has two complex solutions.

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If the Discriminant is 88, how many solutions does the quadratic equation have?

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The quadratic equation has two distinct real solutions.

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What is the formula for the roots of a quadratic equation using the Discriminant?

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The roots can be found using the formula x = (-b ± √(b² - 4ac)) / (2a).