step 1 It's already in standard form, so we can just find, I just read off what our A, B, and C values

4 x^2+8 x-1=0 | Numerade

Name: Problem 50, Chapter 8: Elementary and Intermediate Algebra
Uploaded: 2020-07-19T22:09:46-08:00
Duration: 1 min 11 s
Channel: Charles Carter
Description: 4 x^2+8 x-1=0

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Key Concepts

Standard Form

The standard form of a quadratic equation is ax² + bx + c = 0. Recognizing this form is important because it provides a consistent structure that can be used to identify the necessary coefficients for applying various solution methods such as factoring, completing the square, or the quadratic formula.

Quadratic Formula

The quadratic formula, x = (-b ± ?(b² - 4ac)) / (2a), provides a reliable method for solving any quadratic equation. It directly utilizes the coefficients from the standard form to determine the roots of the equation, making it especially useful when the equation does not factor neatly.

Quadratic Equations

A quadratic equation is a second-degree polynomial equation in one variable, typically expressed as ax² + bx + c = 0, where a, b, and c are coefficients with a not equal to zero. This type of equation produces a parabolic graph and has up to two real roots or solutions.

Discriminant

The discriminant, given by b² - 4ac within the quadratic formula, helps determine the nature of the roots of a quadratic equation. A positive discriminant indicates two distinct real roots, zero indicates one real double root, and a negative discriminant implies that the roots are complex.

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