@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr: a skos:ConceptScheme .
psr:-LK8XNN3X-R
  skos:prefLabel "équation du second degré"@fr, "quadratic equation"@en ;
  a skos:Concept ;
  skos:narrower psr:-MZK5LLKD-P .

psr:-MZK5LLKD-P
  skos:definition """La méthode de <b>complétion du carré</b>, en mathématiques, est un procédé algébrique permettant de réécrire une équation du second degré de la forme <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle ax^{2}+bx+c=0}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>a</mi>         <msup>           <mi>x</mi>           <mrow class="MJX-TeXAtom-ORD">             <mn>2</mn>           </mrow>         </msup>         <mo>+</mo>         <mi>b</mi>         <mi>x</mi>         <mo>+</mo>         <mi>c</mi>         <mo>=</mo>         <mn>0</mn>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle ax^{2}+bx+c=0}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/23e70cfa003f402d108ec04d97983fb62f69536e" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:16.89ex; height:2.843ex;" alt="{\\\\displaystyle ax^{2}+bx+c=0}"></span> sous sa <b>forme canonique</b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle a{\\iggl (}(x+{\\rac {b}{2a}})^{2}-{\\rac {b^{2}-4ac}{4a^{2}}}{\\iggr )}=0}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>a</mi>         <mrow class="MJX-TeXAtom-ORD">           <mrow class="MJX-TeXAtom-OPEN">             <mo maxsize="2.047em" minsize="2.047em">(</mo>           </mrow>         </mrow>         <mo stretchy="false">(</mo>         <mi>x</mi>         <mo>+</mo>         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mi>b</mi>             <mrow>               <mn>2</mn>               <mi>a</mi>             </mrow>           </mfrac>         </mrow>         <msup>           <mo stretchy="false">)</mo>           <mrow class="MJX-TeXAtom-ORD">             <mn>2</mn>           </mrow>         </msup>         <mo>−<!-- − --></mo>         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mrow>               <msup>                 <mi>b</mi>                 <mrow class="MJX-TeXAtom-ORD">                   <mn>2</mn>                 </mrow>               </msup>               <mo>−<!-- − --></mo>               <mn>4</mn>               <mi>a</mi>               <mi>c</mi>             </mrow>             <mrow>               <mn>4</mn>               <msup>                 <mi>a</mi>                 <mrow class="MJX-TeXAtom-ORD">                   <mn>2</mn>                 </mrow>               </msup>             </mrow>           </mfrac>         </mrow>         <mrow class="MJX-TeXAtom-ORD">           <mrow class="MJX-TeXAtom-CLOSE">             <mo maxsize="2.047em" minsize="2.047em">)</mo>           </mrow>         </mrow>         <mo>=</mo>         <mn>0</mn>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle a{\\iggl (}(x+{\\rac {b}{2a}})^{2}-{\\rac {b^{2}-4ac}{4a^{2}}}{\\iggr )}=0}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8982ff6f361871efff4d373610a571ff2927619" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:31.142ex; height:6.343ex;" alt="{\\\\displaystyle a{\\iggl (}(x+{\\rac {b}{2a}})^{2}-{\\rac {b^{2}-4ac}{4a^{2}}}{\\iggr )}=0}"></span>, ou de factoriser le polynôme <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle ax^{2}+bx+c}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>a</mi>         <msup>           <mi>x</mi>           <mrow class="MJX-TeXAtom-ORD">             <mn>2</mn>           </mrow>         </msup>         <mo>+</mo>         <mi>b</mi>         <mi>x</mi>         <mo>+</mo>         <mi>c</mi>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle ax^{2}+bx+c}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/126c6935d3dd9f1c1da0c388ca2799be4f6f237c" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:12.629ex; height:2.843ex;" alt="{\\\\displaystyle ax^{2}+bx+c}"></span>. L'idée est de faire apparaître un carré sous forme d'identité remarquable, puis par exemple d’en extraire la racine carrée. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Compl%C3%A9tion_du_carr%C3%A9">https://fr.wikipedia.org/wiki/Compl%C3%A9tion_du_carr%C3%A9</a>)"""@fr, """In elementary algebra, <b>completing the square</b> is a technique for converting a quadratic polynomial of the form <div class="mwe-math-element"><div class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle ax^{2}+bx+c}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>a</mi>         <msup>           <mi>x</mi>           <mrow class="MJX-TeXAtom-ORD">             <mn>2</mn>           </mrow>         </msup>         <mo>+</mo>         <mi>b</mi>         <mi>x</mi>         <mo>+</mo>         <mi>c</mi>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle ax^{2}+bx+c}</annotation>   </semantics> </math></div><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/126c6935d3dd9f1c1da0c388ca2799be4f6f237c" class="mwe-math-fallback-image-display mw-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:12.629ex; height:2.843ex;" alt="{\\\\displaystyle ax^{2}+bx+c}"></div> to the form <div class="mwe-math-element"><div class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle a(x-h)^{2}+k}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>a</mi>         <mo stretchy="false">(</mo>         <mi>x</mi>         <mo>−<!-- − --></mo>         <mi>h</mi>         <msup>           <mo stretchy="false">)</mo>           <mrow class="MJX-TeXAtom-ORD">             <mn>2</mn>           </mrow>         </msup>         <mo>+</mo>         <mi>k</mi>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle a(x-h)^{2}+k}</annotation>   </semantics> </math></div><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/200edeeb689ffad926fb3f67027786daea98d10d" class="mwe-math-fallback-image-display mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.654ex; height:3.176ex;" alt="{\\\\displaystyle a(x-h)^{2}+k}"></div> for some values of <i>h</i> and <i>k</i>. In other words, completing the square places a perfect square trinomial inside of a quadratic expression. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Completing_the_square">https://en.wikipedia.org/wiki/Completing_the_square</a>)"""@en ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Compl%C3%A9tion_du_carr%C3%A9>, <https://en.wikipedia.org/wiki/Completing_the_square> ;
  skos:inScheme psr: ;
  a skos:Concept ;
  dc:created "2023-09-21"^^xsd:date ;
  skos:prefLabel "complétion du carré"@fr, "completing the square"@en ;
  dc:modified "2024-10-18"^^xsd:date ;
  skos:broader psr:-LK8XNN3X-R .