<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="stack">
    <name>
      <text>PT.1.5 (Example of a quadratic with given roots)</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>Give an example of a quadratic function which has roots \(x={@r1@}\) and \(x={@r2@}\).</p><p>\(q(x)=\) [[input:ans1]][[validation:ans1]]</p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>Since the roots are&nbsp;\(x={@r1@}\) and \(x={@r2@}\), this means the quadratic can be factorised as \( {@(x-r1)*(x-r2)@} \).</p>]]></text>
    </generalfeedback>
    <defaultgrade>2</defaultgrade>
    <penalty>0.1</penalty>
    <hidden>0</hidden>
    <idnumber/>
    <stackversion>
      <text>2020070100</text>
    </stackversion>
    <questionvariables>
      <text>r1:rand_range(-9,-1,1);
r2:rand_with_prohib(1,9,[-r1]);
ta1:(x-r1)*(x-r2);

w1: (x+r1)*(x+r2);
w2: (x+r1)*(x-r2);
w3: (x-r1)*(x+r2);</text>
    </questionvariables>
    <specificfeedback format="html">
      <text><![CDATA[<p>[[feedback:prt1]]<br></p>]]></text>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>{@(x-r1)*(x-r2)@}</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>none</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>ta1</tans>
      <boxsize>10</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>5</insertstars>
      <syntaxhint/>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords/>
      <allowwords/>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
      <checkanswertype>0</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options/>
    </input>
    <prt>
      <name>prt1</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackstyle>1</feedbackstyle>
      <feedbackvariables>
        <text/>
      </feedbackvariables>
      <node>
        <name>0</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>polynomialp(ans1,[x])</sans>
        <tans>true</tans>
        <testoptions/>
        <quiet>1</quiet>
        <truescoremode>=</truescoremode>
        <truescore>0.0000000</truescore>
        <truepenalty/>
        <truenextnode>1</truenextnode>
        <trueanswernote>prt1-1-T</trueanswernote>
        <truefeedback format="html">
          <text/>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prt1-1-F</falseanswernote>
        <falsefeedback format="html">
          <text><![CDATA[<p>Your answer should be a polynomial in \(x\)!&nbsp;</p>]]></text>
        </falsefeedback>
      </node>
      <node>
        <name>1</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>degree(ans1,x)</sans>
        <tans>2</tans>
        <testoptions/>
        <quiet>1</quiet>
        <truescoremode>+</truescoremode>
        <truescore>0.2000000</truescore>
        <truepenalty/>
        <truenextnode>2</truenextnode>
        <trueanswernote>prt1-2-T</trueanswernote>
        <truefeedback format="html">
          <text/>
        </truefeedback>
        <falsescoremode>-</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>2</falsenextnode>
        <falseanswernote>prt1-2-F</falseanswernote>
        <falsefeedback format="html">
          <text><![CDATA[<p>Your polynomial should be a quadratic, but in fact the degree of your polynomial is {@degree(ans1,x)@}!</p>]]></text>
        </falsefeedback>
      </node>
      <node>
        <name>2</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>ev(ans1,x=r1)</sans>
        <tans>0</tans>
        <testoptions/>
        <quiet>1</quiet>
        <truescoremode>+</truescoremode>
        <truescore>0.4000000</truescore>
        <truepenalty/>
        <truenextnode>3</truenextnode>
        <trueanswernote>prt1-3-T</trueanswernote>
        <truefeedback format="html">
          <text/>
        </truefeedback>
        <falsescoremode>-</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>4</falsenextnode>
        <falseanswernote>prt1-3-F</falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
      <node>
        <name>3</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>ev(ans1,x=r2)</sans>
        <tans>0</tans>
        <testoptions/>
        <quiet>1</quiet>
        <truescoremode>+</truescoremode>
        <truescore>0.4000000</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prt1-4-T</trueanswernote>
        <truefeedback format="html">
          <text/>
        </truefeedback>
        <falsescoremode>-</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>5</falsenextnode>
        <falseanswernote>prt1-4-F</falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
      <node>
        <name>4</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>ev(ans1,x=-r1)</sans>
        <tans>0</tans>
        <testoptions/>
        <quiet>0</quiet>
        <truescoremode>+</truescoremode>
        <truescore>0.0000000</truescore>
        <truepenalty/>
        <truenextnode>3</truenextnode>
        <trueanswernote>prt1-5-T</trueanswernote>
        <truefeedback format="html">
          <text><![CDATA[<p>Your quadratic should have a root at \(x = {@r1@}\) but your quadratic has a root at&nbsp;\(x={@-r1@}\).</p>]]></text>
        </truefeedback>
        <falsescoremode>-</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>3</falsenextnode>
        <falseanswernote>prt1-5-F</falseanswernote>
        <falsefeedback format="html">
          <text><![CDATA[<p>Your quadratic should have a root at \(x = {@r1@}\).<br></p>]]></text>
        </falsefeedback>
      </node>
      <node>
        <name>5</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>ev(ans1,x=-r2)</sans>
        <tans>0</tans>
        <testoptions/>
        <quiet>0</quiet>
        <truescoremode>+</truescoremode>
        <truescore>0.0000000</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prt1-6-T</trueanswernote>
        <truefeedback format="html">
          <text><![CDATA[<p>Your quadratic should have a root at \(x = {@r2@}\) but your quadratic has a root at&nbsp;\(x={@-r2@}\).<br></p>]]></text>
        </truefeedback>
        <falsescoremode>-</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prt1-6-F</falseanswernote>
        <falsefeedback format="html">
          <text><![CDATA[<p>Your quadratic should have a root at \(x = {@r2@}\).<br></p>]]></text>
        </falsefeedback>
      </node>
    </prt>
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    <deployedseed>28657607</deployedseed>
    <deployedseed>222717951</deployedseed>
    <deployedseed>1003226819</deployedseed>
    <deployedseed>286749951</deployedseed>
    <deployedseed>2003348786</deployedseed>
    <deployedseed>1098082052</deployedseed>
    <qtest>
      <testcase>1</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>ta1</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt1-4-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>2</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>w1</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>0.2000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt1-6-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>3</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>w2</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>0.6000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt1-4-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>4</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>w3</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>0.6000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt1-6-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>5</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>ta1+1</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>0.2000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt1-6-F</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>6</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>x*ta1</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>0.8000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt1-4-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>7</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>sin(x)*ta1</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt1-1-F</expectedanswernote>
      </expected>
    </qtest>
  </question>
</quiz>
