Solving 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 are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that satisfy the equation, meaning they make the equation equal 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 does the discriminant of a quadratic equation indicate?

Back

The discriminant, given by b² - 4ac, indicates the nature of the roots: if positive, there are two distinct real roots; if zero, there is one real root; if negative, there are two complex roots.

Front

How do you factor a quadratic equation?

Back

To factor a quadratic equation, find two numbers that multiply to ac (the product of a and c) and add to b (the coefficient of x).

Front

Solve the quadratic equation: x² + 7x + 12 = 0

Back

x = -3, x = -4

Front

Solve the quadratic equation: x² - 2x - 15 = 0

Back

x = 5, x = -3

Front

Solve the quadratic equation: x² + 4x - 32 = 0

Back

x = -8, x = 4

Front

Solve the quadratic equation: x² + 13x + 36 = 0

Back

x = -9, x = -4

Front

Solve the quadratic equation: x² - 13x + 30 = 0

Back

x = 10, x = 3