Chapter 2: Quadratic Equations - Introduction

After studying this unit students will be able to:

Algebra is your trusted tool that helps you carry out of various activities of daily importance. There is hardly any line of work that does not employ the concept of algebra. We will look at the variables and equation, you surely will not be wondered about why you need to leave there in a nutshell. Algebra and equations prepare you for hardly all aspects of life and stays with you right from your infanthood to your adulthood.

Quadratic Equations

Saelem wants to build a swimming pool surrounded by a sidewalk of uniform width. He wants the dimensions of the pool and sidewalk to be 16 meters by 20 meters. The pool has an area of 192 square meters. How wide should the sidewalk be?

Let $x$ meters be the width of the sidewalk.

The length of a pool is $20 - 2x$ meters.

The width of the pool is $16 - 2x$ meters.

The area of the pool can be expressed as the product of the length and width.

Area $=$ Length $\times$$\times$ Width

The area of the pool can be expressed as $4x^{2} - 72x + 320$ square meters. Since the area of the pool is 192 square meters, replacing area with 192 results in the equation $192 = 4x^{2} - 72x + 320$ . Saelem would probably never use a quadratic equation like $192 = 4x^{2} - 72x + 320$ to express area of a pool. However, in this unit we will study many other formulas in science and business that involve this type of equations.

Quadratic Equation

It is an equation that can be written in the form of $ax^{2} + bx + c = 0$ , where $a \neq 0$ . We say that equations like this have a degree of 2. Since the greatest exponent of the variable is 2. We observe that this quadratic equation only has one variable and all the exponents are positive.

Standard Quadratic Equation