Question

Solve using the quadratic formula. $$ 4 x_{2}+2 x+1=0 $$

   Solve using the quadratic formula.
$$
4 x_{2}+2 x+1=0
$$

Elementary Algebra

Elementary Algebra

John Redden 1st Edition

Chapter 9, Problem 74

Instant Answer

Solved by Expert Victor Salazar

02/04/2022

Step 1

In this case, we have a = 4, b = 2, and c = 1. Show more…

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Solve using the quadratic formula. $$ 4 x_{2}+2 x+1=0 $$

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Key Concepts

Discriminant

The discriminant, found within the quadratic formula as b² - 4ac, plays a crucial role in determining the nature of the roots of a quadratic equation. A positive discriminant indicates two distinct real roots, zero indicates one real repeated root, and a negative discriminant suggests the presence of two complex conjugate roots.

Quadratic Equation

A quadratic equation is a second-degree polynomial equation generally expressed in the form ax² + bx + c = 0, where a, b, and c are constants and a is not zero. This type of equation is foundational in algebra and arises in various mathematical and real-world applications.

Standard Form

Expressing a quadratic equation in its standard form, ax² + bx + c = 0, organizes the terms in descending order of degree. This form is essential for identifying the coefficients used in techniques such as factoring, completing the square, or applying the quadratic formula.

Quadratic Formula

The quadratic formula, x = (-b ± ?(b² - 4ac)) / (2a), is a universal method for solving any quadratic equation. By substituting the coefficients from the standard form into the formula, one can determine the roots of the equation, regardless of whether they are real or complex.

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