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 does it mean to solve a quadratic equation by factoring?

Back

Solving a quadratic equation by factoring involves rewriting the equation in the form (x - p)(x - q) = 0, where p and q are the roots of the equation.

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 identify a, b, and c in a quadratic equation?

Back

In the quadratic equation ax² + bx + c = 0, 'a' is the coefficient of x², 'b' is the coefficient of x, and 'c' is the constant term.

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 distinct real roots; if zero, one real root; if negative, no real roots.

Front

Solve by factoring: x² - 13x + 42 = 0

Back

x = 6 or x = 7.

Front

Solve by factoring: x² - 9x + 20 = 0

Back

x = 4 and x = 5.

Front

Determine a, b, and c for the equation 4x² - 8x = 3

Back

a = 4, b = -8, c = -3.

Front

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

Back

x = -9 and x = -4.

Front

Solve using the Quadratic Formula: 4x² + x - 95 = 0

Back

x = 4.75 or x = -5.