<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="stack">
    <name>
      <text>Quadratic_1</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>Solve the following quadratic equation: \[{@pol@} = 0\] Hint: give your answer as a set, e.g. {5, 21+3i}. Marks are only given for a complete and correct answer. <br /> The solutions are:[[input:ans1]] [[validation:ans1]]</p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>Using the quadratic formula \[z=\frac{-b±\sqrt{b^2-4ac}}{2a}\] for the solutions of the equation \(az^2+bz+c=0\) to solve {@pol@} gives \[z= \frac{{@-bcoeff@}\pm\sqrt{{@bcoeff@}^2-4\times{@acoeff@}\times{@ccoeff@}}}{@2*acoeff@}=\frac{{@-bcoeff@}\pm{@sqrt(bcoeff^2-4*acoeff*ccoeff)@}}{@2*acoeff@}={@sol@}\]</p>]]></text>
    </generalfeedback>
    <defaultgrade>1</defaultgrade>
    <penalty>0</penalty>
    <hidden>0</hidden>
    <idnumber/>
    <stackversion>
      <text/>
    </stackversion>
    <questionvariables>
      <text>n1:rand(10);
 n2:rand(8)+ 2;
 pol:expand((z-n1-n2*i)*(z-n1+n2*i));
 sol:{n1 + i*n2, n1 - i*n2};
 wrongsol:{n1 + n2, n1 - n2};
 acoeff:coeff(pol,z,2);
 bcoeff:coeff(pol,z,1);
 ccoeff:coeff(pol,z,0);</text>
    </questionvariables>
    <specificfeedback format="html">
      <text><![CDATA[<p>[[feedback:Result]]</p>]]></text>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>{@pol@}=0
  gives {@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>1.0000000</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>1</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>
      <node>
        <name>1</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>ans1</sans>
        <tans>wrongsol</tans>
        <testoptions/>
        <quiet>1</quiet>
        <truescoremode>+</truescoremode>
        <truescore>0.0000000</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>Result-1-T </trueanswernote>
        <truefeedback format="html">
          <text><![CDATA[<p>Have you forgotten the square root of -1 is i?</p>]]></text>
        </truefeedback>
        <falsescoremode>-</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>Result-1-F </falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
    </prt>
    <deployedseed>1916988899</deployedseed>
    <deployedseed>973411243</deployedseed>
    <deployedseed>1008146382</deployedseed>
    <deployedseed>1411446220</deployedseed>
    <deployedseed>1216426991</deployedseed>
    <deployedseed>708865721</deployedseed>
    <deployedseed>1037681207</deployedseed>
    <deployedseed>351661046</deployedseed>
    <deployedseed>1448520258</deployedseed>
    <deployedseed>1986400524</deployedseed>
    <deployedseed>2006147804</deployedseed>
    <deployedseed>1218749712</deployedseed>
    <deployedseed>1627981802</deployedseed>
    <deployedseed>142342794</deployedseed>
    <deployedseed>1310741257</deployedseed>
    <deployedseed>573964632</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>{n1 + i*n2-1, n1 - i*n2-1}</value>
      </testinput>
      <expected>
        <name>Result</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>Result-1-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-1-T</expectedanswernote>
      </expected>
    </qtest>
  </question>
</quiz>
