Quadratic Formula & Discriminant Review

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What is the Quadratic Formula?

Back

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

Front

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. It determines the nature of the roots.

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What does a positive Discriminant indicate?

Back

A positive Discriminant indicates that there are two distinct real solutions to the quadratic equation.

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What does a negative Discriminant indicate?

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A negative Discriminant indicates that there are no real solutions, only complex solutions.

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What does a Discriminant of zero indicate?

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A Discriminant of zero indicates that there is exactly one real solution, also known as a repeated or double root.

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How do you calculate the Discriminant?

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The Discriminant is calculated using the formula: D = b² - 4ac, where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.

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If the Discriminant is -2, how many real solutions are there?

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There are no real solutions.

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If the Discriminant is 0, how many real solutions are there?

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There is one real solution.

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What does the Discriminant tell us about the solutions of a quadratic equation?

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The Discriminant tells us the number and type of solutions: two real solutions (D > 0), one real solution (D = 0), or no real solutions (D < 0).

Front

What is the significance of the coefficients a, b, and c in the quadratic equation?

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The coefficients a, b, and c determine the shape and position of the parabola represented by the quadratic equation y = ax² + bx + c.