step 1 There are several ways that we can factor or solve this, but what we're going to do is grouping.

3 x^2+10 x-8=0 | Numerade

Name: Problem 6, Chapter 8: Elementary and Intermediate Algebra
Uploaded: 2020-07-10T16:14:48-08:00
Duration: 1 min 53 s
Channel: Victoria Karaluz
Description: 3 x^2+10 x-8=0

Key Concepts

Completing the Square

Completing the square is a technique for rewriting a quadratic equation in the form (x + p)² = q. This method transforms the equation into a perfect square trinomial, making it easier to solve by isolating the variable, and it also lays the groundwork for understanding the derivation of the quadratic formula.

Discriminant

The discriminant of a quadratic equation, found in the expression b² - 4ac within the quadratic formula, determines the nature and number of the roots. A positive discriminant indicates two distinct real roots, zero indicates one real repeated root, and a negative discriminant indicates two complex conjugate roots, providing important insights into the behavior of the quadratic function.

Factoring

Factoring is an algebraic method of solving quadratic equations by expressing the quadratic polynomial as a product of two linear factors. This method is efficient when the quadratic expression can be factored easily and provides an alternative to using the quadratic formula.

Quadratic Formula

The quadratic formula, x = (-b ± ?(b² - 4ac)) / (2a), is a general solution method for solving quadratic equations. It provides a systematic way to find the roots of any quadratic equation by substituting the coefficients a, b, and c from the equation, and it is especially useful when the equation does not factor easily.

Quadratic Equation

A quadratic equation is a second-degree polynomial equation in one variable, typically written in the form ax² + bx + c = 0, where a, b, and c are constants and a is nonzero. These equations are fundamental in algebra and appear in a wide range of mathematical contexts, including modeling physical processes and solving optimization problems.

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