Solve Quadratic Equations

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?

Back

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

Front

What does it mean to 'complete the square'?

Back

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form (x - p)² = q, making it easier to solve for x.

Front

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, express the quadratic equation in the form (x - r)(x - s) = 0, where r and s are the roots, then set each factor to zero.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots 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?

Back

A positive discriminant indicates that the quadratic equation has two distinct real roots.

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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 root (a repeated root).

Front

What does a negative discriminant indicate?

Back

A negative discriminant indicates that the quadratic equation has two complex (imaginary) roots.

Front

How do you solve x² - 2x = 3 by completing the square?

Back

Rearranging gives x² - 2x - 3 = 0. Completing the square results in (x - 1)² = 4, leading to x = -1, 3.