finding solutions to quadratics

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a quadratic equation?

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The standard form of a quadratic equation is ax² + bx + c = 0.

Front

What does it mean to find the zeros of a quadratic equation?

Back

Finding the zeros of a quadratic equation means determining the values of x that make the equation equal to zero.

Front

What is the maximum number of solutions a quadratic equation can have?

Back

A quadratic equation can have a maximum of 2 solutions.

Front

What is the quadratic formula?

Back

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

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, b² - 4ac, which determines the nature of the roots.

Front

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 zero discriminant indicate?

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A zero discriminant 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 (the solutions are complex).

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How do you solve a quadratic equation by factoring?

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To solve by factoring, express the quadratic in the form (x - p)(x - q) = 0, then set each factor to zero: x - p = 0 and x - q = 0.