Understanding And Solving 2X² + 5X + 3 = 0 In Relaxed English

Example 3 Find roots of 2x2 5x + 3 = 0 by factorization from www.teachoo.com

Introduction

As a professional teacher, it is essential to explain mathematical concepts in a way that students can understand quickly. One such concept is solving quadratic equations, which can be a challenging task for many students. In this article, we will focus on solving a quadratic equation of the form 2x² + 5x + 3 = 0 in relaxed English.

What is a Quadratic Equation?

A quadratic equation is an equation of the form ax² + bx + c = 0, where a, b, and c are constants. In this case, the quadratic equation is 2x² + 5x + 3 = 0. The first step in solving this equation is to identify the values of a, b, and c.

Identifying the Values of a, b, and c

In the quadratic equation 2x² + 5x + 3 = 0, a = 2, b = 5, and c = 3. It is essential to identify these values before proceeding with the solution.

Solving the Quadratic Equation

To solve the quadratic equation 2x² + 5x + 3 = 0, we will use the quadratic formula, which is given by: x = (-b ± sqrt(b² - 4ac)) / 2a

Using the Quadratic Formula

Substituting the values of a, b, and c into the quadratic formula, we get: x = (-5 ± sqrt(5² - 4(2)(3))) / 2(2) Simplifying the equation, we get: x = (-5 ± sqrt(1)) / 4 x = (-5 ± 1) / 4 Therefore, x has two values: x₁ = (-5 + 1) / 4 = -3/2 x₂ = (-5 - 1) / 4 = -1

Verifying the Solution

To verify the solution, we can substitute the values of x₁ and x₂ into the original equation and check if they satisfy it. Substituting x₁, we get: 2(-3/2)² + 5(-3/2) + 3 = 0 Simplifying the equation, we get: 9/2 - 15/2 + 3 = 0 0 = 0 Therefore, x₁ is a valid solution. Similarly, substituting x₂, we get: 2(-1)² + 5(-1) + 3 = 0 Simplifying the equation, we get: 2 - 5 + 3 = 0 0 = 0 Therefore, x₂ is also a valid solution.

Conclusion

In conclusion, solving a quadratic equation of the form 2x² + 5x + 3 = 0 involves identifying the values of a, b, and c and using the quadratic formula to find the values of x. In this article, we have explained the steps involved in solving this equation in relaxed English, making it easier for students to understand.