2.4 - Solving Equations Algebraically

# 2.4 - Solving Equations Algebraically -

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<?xml version="1.0" encoding="utf-8"?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <title>2.4 - Solving Equations Algebraically</title> <link href=". ./m116.css" rel="stylesheet" type="text/css" /> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> </head> <body> <h1>2.4 - Solving Equations Algebraically</h1> <h2>Quadratic Equations</h2> <p>A quadratic equation is an equation that can be written as Ax<sup>2</sup> + Bx + C = 0 where A&ne;0. This form is called the standard form. </p> <p>There are four ways to solve a quadratic equation.</p> <h2>Factoring</h2> <p>Works well when the quadratic can easily be factored. </p> <p>Some of you were taught the trial and error method of factoring. Others of you were taught the <a href=". ./. ./. ./misc/acmeth.html">AC Method of Factoring</a>. The AC Method is explained elsewhere if you want to review or learn it. </p> <p>The idea behind factoring is to place the equation into standard form, and then factor the left hand side into two factors (x-a) and (x-b). The solutions to the equation are then x=a and x=b. The factors will of course vary if A&ne;1. Factoring works because there is a rule which says if the product of two factors is zero, then one of the factors must be zero.</p> <h2>Extraction of Roots</h2> <p>Works well when there is no linear term, that is, when B=0. </p> <p>The extraction of roots is called the square root principle by your text. The goal here is to get the squared variable term by itself on one side and a non-negative constant on the other side. </p> <p>The square root of both sides is then taken. Remember that the square root of x<sup>2</sup> is the absolute value of x. When you solve an equation involving an absolute value, you will get a plus and minus in the solution. Too often, we bypass the step with the absolute value in it and go straight to the plus/minus phase. This is okay, as long as we remember the reason.</p> <h2>Completing the Square</h2> <p>Works well when the leading coefficient A is 1 and B is even. </p>

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## This note was uploaded on 10/18/2011 for the course MAT 1033 taught by Professor Brown during the Spring '10 term at Valencia.

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2.4 - Solving Equations Algebraically -

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