Table of Contents

1. Introduction
2. How to Approach Quadratic Equations

Introduction

A polynomial is an expression constructed from variables and constants.

Example

The variables a, b, and c are constants. The GMAT often tests first and second order polynomials, so a clear understanding of how to deal with these mathematical structures is very important.

How to Approach Quadratic Equations

A quadratic equation is essentially a polynomial of the second order. They can be found in the form:

The GMAT should never ask you to solve a polynomial that is complex enough to require use of the quadratic equation. There will always be an easier method to find the answer.

The simplest method to solve a quadratic equation is to use a technique called factoring. Follow this approach:

1. Express the statement in quadratic form, meaning move all of the terms to one side of the equation so that the expression equals zero
2. Once the statement is in the quadratic form shown above, find two numbers that have a sum equal to constant b and a product equal to constant c.
3. Write out the new statement in factored form
4. Solve for variables
5. Test the solution

Example

In the example above, the only solution to this equation is x = 4. x = -1 is not a solution to the equation

Example

Since we can’t solve this equation if it is expressed in quadratic form, simplify this problem as much as possible in its current form.

This essentially becomes an exponent problem, so treat it as such:

x is equal to √18-1 and -√18-1

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