LT #9 Solving Quadratics

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 solutions of a quadratic equation called?

Back

The solutions of a quadratic equation are called roots, x-intercepts, or zeros.

Front

How do you find the roots of a quadratic equation using factoring?

Back

To find the roots by factoring, express the quadratic in the form (x - p)(x - q) = 0, where p and q are the roots.

Front

What is the quadratic formula?

Back

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

Front

What does the discriminant of a quadratic equation indicate?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if > 0, two distinct real roots; if = 0, one real root; if < 0, two complex roots.

Front

Solve: 2x² + 17x + 21 = 0

Back

The solutions are x = -7 and x = -3/2.

Front

True or False: The solution, root, x-intercept, and zero of a quadratic equation are all the same thing.

Back

True.

Front

Solve by factoring: x² - 5x + 6 = 0

Back

The solutions are x = 3 and x = 2.

Front

Identify the solutions to: 2x(x - 4)(x + 2) = 0

Back

The solutions are x = 0, x = -2, and x = 4.

Front

Solve: a² + 2a - 24 = 0

Back

The solutions are a = -6 and a = 4.