step 1 Right, let's look at the equation x squared over 2 plus 2 x, sorry, plus 2 over 3 equals 0. So t

X^2-(1)/(3) x=2 | Numerade

Name: Problem 46, Chapter 8: Elementary and Intermediate Algebra
Uploaded: 2020-06-18T21:54:00-08:00
Duration: 2 min 29 s
Channel: Teresa Liang
Description: x^2-(1)/(3) x=2

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Key Concepts

Quadratic Equation

A quadratic equation is a second-degree polynomial equation, typically defined in the form ax² + bx + c = 0, where a, b, and c are constants and a ? 0. It is a fundamental concept in algebra that models parabolic relationships and appears frequently in various applications across mathematics and science.

Standard Form

The standard form of a quadratic equation is ax² + bx + c = 0. This form is essential because it provides a structured framework that facilitates the application of various solution methods, such as factoring, the quadratic formula, or completing the square.

Quadratic Formula

The quadratic formula is a universal method for solving quadratic equations and is given by x = (-b ± ?(b² - 4ac)) / (2a). It is particularly useful when the equation is not easily factorable, as it directly computes the roots of any quadratic equation.

Discriminant

The discriminant is the part of the quadratic formula under the square root, expressed as b² - 4ac. It determines the nature of the roots: if it is positive, the equation has two distinct real solutions; if it is zero, there is exactly one real solution; and if it is negative, the equation has two complex solutions.

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