Solving Quadratics (All Methods)

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 are the methods to solve quadratic equations?

Back

The main methods to solve quadratic equations are factoring, completing the square, and using the quadratic formula.

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 does it mean to factor a quadratic equation?

Back

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

Front

What is the zero product property?

Back

The zero product property states that if the product of two factors is zero, then at least one of the factors must be zero.

Front

How do you complete the square?

Back

To complete the square, rearrange the equation to isolate the constant term, then add and subtract the square of half the coefficient of x.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the expression b² - 4ac in the quadratic formula, which determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, two complex roots.

Front

Solve the quadratic equation: 2x² - x - 3 = 0

Back

x = 3/2 and x = -1.

Front

Solve by square root: 4m² - 100 = 0

Back

m = 5 and m = -5.

Front

Complete the square for: x² + 6x = 5

Back

(x + 3)² = 14.