Discriminant & Quadratic Formula

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What is the Discriminant in a quadratic equation?

Back

The Discriminant is the part of the quadratic formula under the square root, given by b² - 4ac, which determines the nature and number of solutions of the quadratic equation ax² + bx + c = 0.

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What does a positive Discriminant indicate?

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

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What does a Discriminant of zero indicate?

Back

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

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What does a negative Discriminant indicate?

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

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How do you calculate the Discriminant for the equation 2x² + 3x - 5 = 0?

Back

The Discriminant is calculated as b² - 4ac = (3)² - 4(2)(-5) = 9 + 40 = 49.

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What is the Quadratic Formula?

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The Quadratic Formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation.

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If the Discriminant is 0, what is the nature of the roots?

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The roots are real and equal (or repeated).

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What is the Discriminant of the equation x² - 4x + 4 = 0?

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The Discriminant is 0, indicating one real solution.

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Calculate the Discriminant for the equation 3x² + 6x + 2 = 0.

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The Discriminant is b² - 4ac = (6)² - 4(3)(2) = 36 - 24 = 12.

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What is the significance of the x-intercept in relation to the roots of a quadratic equation?

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The x-intercepts of a quadratic function are the points where the graph intersects the x-axis, which correspond to the real roots of the equation.