All methods of solving quadratic equations

Front

What is a quadratic equation?

Back

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

Front

What are the methods to solve quadratic equations?

Back

1. Factoring 2. Completing the square 3. Quadratic formula 4. Graphing

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

How do you complete the square for the equation x² - 6x + 5 = 0?

Back

1. Move the constant to the other side: x² - 6x = -5 2. Add (6/2)² = 9 to both sides: x² - 6x + 9 = 4 3. Factor: (x - 3)² = 4 4. Solve: x - 3 = ±2, so x = 5 or x = 1.

Front

What does it mean to factor a quadratic equation?

Back

Factoring a quadratic equation means expressing it as a product of two binomials, such as (x - p)(x - q) = 0, where p and q are the roots.

Front

Solve by factoring: x² - 5x + 6 = 0.

Back

(x - 2)(x - 3) = 0; x = 2 or x = 3.

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. It 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?

Back

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 no real roots (the roots are complex).