<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="stack">
    <name>
      <text>Quartic_1</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>If \(\ {@n1@}\) + \({@n2@} i\ \) is a root of the quartic equation \[{@pol@} = 0,\] find the remaining roots. Hint: give your answer as a set, e.g. {5, 9, 21+3*i}. <br />The remaining solutions are: [[input:ans1]] <br />Marks are only given for a complete and correct answer. [[validation:ans1]]</p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>Given \(\ {@n1@}+{@n2@}i\ \) is a root of the equation \({@pol@} = 0\), then \(\ {@n1@}-{@n2@}i\ \) is a root as well and \[ {@quadratic1@} \] is a factor</p>
<p>Dividing by \({@quadratic1@}\) gives \[{@quadratic2=0@}\] and hence \[{@(z-n3)*(z-n4)@}=0\]. <br /> Therefore the remaining roots are \({@sol@}\)</p>]]></text>
    </generalfeedback>
    <defaultgrade>1</defaultgrade>
    <penalty>0</penalty>
    <hidden>0</hidden>
    <idnumber/>
    <stackversion>
      <text/>
    </stackversion>
    <questionvariables>
      <text>n1:rand(9)+1;
 n2:rand(8)+2;
 n3:rand(11)+1;
 n4:rand(5)+1;
 pol:expand((z-n1-n2*i)*(z-n1+n2*i)*(z-n3)*(z-n4));
 quadratic1:expand((z-n1-n2*i)*(z-n1+n2*i));
 quadratic2:expand((z-n3)*(z-n4));
 sol:{n1 - i*n2, n3, n4};
 wrongsol:{n1+ i*n2, n3, n4};</text>
    </questionvariables>
    <specificfeedback format="html">
      <text><![CDATA[<p>[[feedback:Result]]</p>]]></text>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>\({@pol@}\) has roots of \({@sol@}\)</text>
    </questionnote>
    <questiondescription format="moodle_auto_format">
      <text/>
    </questiondescription>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <prtcorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Correct answer, well done.]]></text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Your answer is partially correct.]]></text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Incorrect answer.]]></text>
    </prtincorrect>
    <decimals>.</decimals>
    <scientificnotation>*10</scientificnotation>
    <multiplicationsign>dot</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <logicsymbol>lang</logicsymbol>
    <matrixparens>[</matrixparens>
    <isbroken>0</isbroken>
    <variantsselectionseed/>
    <input>
      <name>ans1</name>
      <type>algebraic</type>
      <tans>sol</tans>
      <boxsize>20</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint/>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords>solve</forbidwords>
      <allowwords/>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>1</requirelowestterms>
      <checkanswertype>1</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options/>
    </input>
    <prt>
      <name>Result</name>
      <value>2.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackstyle>1</feedbackstyle>
      <feedbackvariables>
        <text/>
      </feedbackvariables>
      <node>
        <name>0</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>ans1</sans>
        <tans>sol</tans>
        <testoptions/>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>Result-0-T </trueanswernote>
        <truefeedback format="html">
          <text/>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>Result-0-F </falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
    </prt>
    <deployedseed>783550102</deployedseed>
    <deployedseed>113112737</deployedseed>
    <deployedseed>1029548008</deployedseed>
    <deployedseed>1290488159</deployedseed>
    <deployedseed>393385661</deployedseed>
    <deployedseed>1265666594</deployedseed>
    <deployedseed>1117659000</deployedseed>
    <deployedseed>296152977</deployedseed>
    <deployedseed>812433728</deployedseed>
    <deployedseed>688791395</deployedseed>
    <deployedseed>434068829</deployedseed>
    <deployedseed>381584543</deployedseed>
    <deployedseed>104397634</deployedseed>
    <deployedseed>1217339387</deployedseed>
    <deployedseed>989224623</deployedseed>
    <qtest>
      <testcase>1</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>sol</value>
      </testinput>
      <expected>
        <name>Result</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>Result-0-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>2</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>{0,1,2}</value>
      </testinput>
      <expected>
        <name>Result</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>Result-0-F</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>3</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>wrongsol</value>
      </testinput>
      <expected>
        <name>Result</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>Result-0-F</expectedanswernote>
      </expected>
    </qtest>
  </question>
</quiz>
