step 1 In order to solve this equation, the first thing we need to do is factor. So this trinomial fact

Solve. q^2-12 q-13=0

Name: Problem 352, Chapter 7: Elementary Algebra
Uploaded: 2021-07-22T15:37:22-08:00
Duration: 50 s
Channel: Katelyn Vandeaver
Description: Solve. q^2-12 q-13=0

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Key Concepts

Discriminant

The discriminant, given by b² - 4ac in the quadratic formula, is the part under the square root that determines the nature of the roots. A positive discriminant indicates two distinct real roots, zero indicates a single repeated real root, and a negative discriminant indicates two complex conjugate roots.

Factoring

Factoring is a method of rewriting a quadratic equation as a product of two binomial expressions. When a quadratic can be factored easily, this approach allows for a straightforward solution by setting each factor equal to zero and solving for the variable.

Quadratic Equation

A quadratic equation is a second-degree polynomial equation typically written in the standard form ax² + bx + c = 0, where a, b, and c are constants and a is non-zero. Understanding this form is fundamental as it sets the stage for applying various methods to find the equation's roots.

Quadratic Formula

The quadratic formula, x = (-b ± ?(b² - 4ac))/(2a), is a universal method for solving any quadratic equation. It is derived from the process of completing the square and is especially useful when the quadratic does not factor easily, as it directly computes the solutions using the coefficients.

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