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Course: Algebra III / Intermediate Algebra
Topic: Nonlinear Equations and Applications
Subtopic: Quadratic Equations I - Root Method

Overview

Quadratic equations (i.e., equations that have an x-squared term but no higher power) can be solved by several methods. The first and foremost is by factoring. But what if the quadratic is not factorable (prime)? Luckily, we can resort to three other methods. These methods will open up a world of real-life applications where the equations are usually not "nice" and factorable.

This lesson covers the root method which can be used only when the quadratic is in the specific form, (expression)2=#. By applying the square root function to the equation, we "undo" the square and are able so solve for x.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 11.2.1 Recognize quadratic equations that can be solved by the root method
• 11.2.2 Solve quadratic equations algebraically by the square root method
• 11.2.3 Know that a plus-or-minus sign is required when applying the square root function to an equation and why
• 11.2.4 Apply the root method to solving applications involving the compound interest formula A=P(1+r)t

Terminology

Define: quadratic, quadratic equation, root method (a.k.a. square root method) of solving a quadratic equation, plus-or-minus sign

Text Notes

You are expected to already know how to solve a polynomial equation algebraically by factoring and using the zero product rule and also graphically by electronically graphing the polynomial and using ZERO to find the x-intercept values.

When using the square root method, be careful that you end up with two answers, i.e. don't forget to include the plus-or-minus sign at the point that you apply the square root function to both sides of the equation. Also, watch for imaginary numbers!