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<document xmlns="http://cnx.rice.edu/cnxml" xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="id9929848">
  <name xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Imaginary Numbers Homework -- Homework: Quadratic Equations and Complex Numbers</name>
  <metadata xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">
  <md:version xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">1.1</md:version>
  <md:created xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">2008/10/16 11:12:24.723 GMT-5</md:created>
  <md:revised xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">2008/12/31 11:37:58.888 US/Central</md:revised>
  <md:authorlist xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">
      <md:author xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="kennyfelder">
      <md:firstname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Kenny</md:firstname>
      
      <md:surname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Felder</md:surname>
      <md:email xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">KFelder@RaleighCharterHS.org</md:email>
    </md:author>
  </md:authorlist>

  <md:maintainerlist xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">
    <md:maintainer xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="kennyfelder">
      <md:firstname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Kenny</md:firstname>
      
      <md:surname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Felder</md:surname>
      <md:email xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">KFelder@RaleighCharterHS.org</md:email>
    </md:maintainer>
  </md:maintainerlist>
  
  <md:keywordlist xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">
    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">algebra</md:keyword>
    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">complex</md:keyword>
    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">complex numbers</md:keyword>
    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">i</md:keyword>
    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">imaginary</md:keyword>
    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">imaginary numbers</md:keyword>
    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">quadratic equations</md:keyword>
    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">quadratics</md:keyword>
  </md:keywordlist>

  <md:abstract xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">This module provides practice problems related to solving quadratics containing imaginary numbers.</md:abstract>
</metadata>
  <content xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">

      <para xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="id8539532">I’m sure you remember the quadratic formula: <m:math><m:mi>x</m:mi>
<m:mo>=</m:mo>
<m:semantics><m:mrow><m:mstyle fontsize="12pt"><m:mrow><m:mfrac><m:mrow><m:mrow><m:mo stretchy="false">−</m:mo><m:mi>b</m:mi></m:mrow><m:mo stretchy="false">±</m:mo><m:msqrt><m:mrow><m:mrow><m:msup><m:mi>b</m:mi><m:mstyle fontsize="8pt"><m:mrow><m:mn>2</m:mn></m:mrow></m:mstyle></m:msup><m:mo stretchy="false">−</m:mo><m:mn>4</m:mn></m:mrow><m:mstyle fontstyle="italic"><m:mrow><m:mtext>ac</m:mtext></m:mrow></m:mstyle></m:mrow></m:msqrt></m:mrow><m:mn>2a</m:mn></m:mfrac></m:mrow></m:mstyle><m:mrow/></m:mrow><m:annotation encoding="StarMath 5.0"> size 12{ {  { - b +-  sqrt {b rSup { size 8{2} }  - 4 ital "ac"} }  over  {2a} } } {}</m:annotation></m:semantics></m:math>. Back when we were doing quadratic equations, if we wound up with a negative number under that square root, we just gave up. But now we can solve these equations!</para>
      <exercise xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="id11884706">
        <problem xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">
          <para xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="id11062359">Use the quadratic formula to solve: <m:math>
<m:mn>2</m:mn>
<m:msup>
<m:mi>x</m:mi>
<m:mn>2</m:mn>
</m:msup>
<m:mo>+</m:mo>
<m:mn>6</m:mn>
<m:mi>x</m:mi>
<m:mo>+</m:mo>
<m:mn>5</m:mn>
<m:mo>=</m:mo>
<m:mn>0</m:mn>
</m:math>.</para>
        </problem>
      </exercise>
      <exercise xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="id9278367">
        <problem xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">
          <para xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="id11549991">Use the quadratic formula to solve: <m:math>
<m:msup>
<m:mi>x</m:mi>
<m:mn>2</m:mn>
</m:msup>
<m:mo>-</m:mo>
<m:mn>2</m:mn>
<m:mi>x</m:mi>
<m:mo>+</m:mo>
<m:mn>5</m:mn>
<m:mo>=</m:mo>
<m:mn>0</m:mn>
</m:math>.</para>
        </problem>
      </exercise>
      <exercise xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="id7747643">
        <problem xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">
          <para xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="id11501733">Check one of your answers to #2.</para>
        </problem>
      </exercise>
      <exercise xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="id11065716">
        <problem xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">
          <para xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="id10731529">Solve by <emphasis xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">completing the square</emphasis>: <m:math>
<m:mn>2</m:mn>
<m:msup>
<m:mi>x</m:mi>
<m:mn>2</m:mn>
</m:msup>
<m:mo>+</m:mo>
<m:mn>10</m:mn>
<m:mi>x</m:mi>
<m:mo>+</m:mo>
<m:mn>17</m:mn>
<m:mo>=</m:mo>
<m:mn>0</m:mn>
</m:math>.</para>
        </problem>
      </exercise>
      <exercise xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="hw9exerciseid">
        <problem xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">
      <list xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="id9184664" type="named-item"><?mark .?>
        <item xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/"><name xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">a</name>In general, what has to be true for a quadratic equation to have <emphasis xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">two non-real roots</emphasis>?</item>
        <item xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/"><name xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">b</name>What is the relationship between the two non-real roots?</item>
        <item xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/"><name xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">c</name>Is it possible to have a quadratic equation with <emphasis xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">one</emphasis> non-real root?</item>
      </list>
        </problem>
      </exercise>

  </content>
</document>
