File:Polynomialdeg3.svg
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Summary
Polynomial of degree 3:
<img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e66c22342f8a6af1d1d1788acab1ca6448e36630" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -4.896ex; margin-bottom: -0.275ex; width:28.274ex; height:11.509ex;" alt=" \begin{align} y&=\tfrac{1}{4}(x+4)(x+1)(x-2)\\ &=\tfrac{1}{4}(x^3+3x^2-6x-8)\\ &=\tfrac{1}{4}x^3+\tfrac{3}{4}x^2-\tfrac{3}{2}x-2 \end{align} "> The roots are 2, -1, and -4.
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 18:24, 4 January 2017 | | 400 × 400 (737 bytes) | 127.0.0.1 (talk) | <p>Polynomial of degree 3: </p> <p><span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"><mtr><mtd><mi>y</mi></mtd><mtd><mi></mi><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="false" scriptlevel="0"><mfrac><mn>1</mn><mn>4</mn></mfrac></mstyle></mrow><mo stretchy="false">(</mo><mi>x</mi><mo>+</mo><mn>4</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi>x</mi><mo>−<!-- − --></mo><mn>2</mn><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="false" scriptlevel="0"><mfrac><mn>1</mn><mn>4</mn></mfrac></mstyle></mrow><mo stretchy="false">(</mo><msup><mi>x</mi><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow></msup><mo>+</mo><mn>3</mn><msup><mi>x</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>−<!-- − --></mo><mn>6</mn><mi>x</mi><mo>−<!-- − --></mo><mn>8</mn><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="false" scriptlevel="0"><mfrac><mn>1</mn><mn>4</mn></mfrac></mstyle></mrow><msup><mi>x</mi><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow></msup><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="false" scriptlevel="0"><mfrac><mn>3</mn><mn>4</mn></mfrac></mstyle></mrow><msup><mi>x</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>−<!-- − --></mo><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="false" scriptlevel="0"><mfrac><mn>3</mn><mn>2</mn></mfrac></mstyle></mrow><mi>x</mi><mo>−<!-- − --></mo><mn>2</mn></mtd></mtr></mtable></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}y&={\tfrac {1}{4}}(x+4)(x+1)(x-2)\\&={\tfrac {1}{4}}(x^{3}+3x^{2}-6x-8)\\&={\tfrac {1}{4}}x^{3}+{\tfrac {3}{4}}x^{2}-{\tfrac {3}{2}}x-2\end{aligned}}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e66c22342f8a6af1d1d1788acab1ca6448e36630" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -4.896ex; margin-bottom: -0.275ex; width:28.274ex; height:11.509ex;" alt=" \begin{align} y&=\tfrac{1}{4}(x+4)(x+1)(x-2)\\ &=\tfrac{1}{4}(x^3+3x^2-6x-8)\\ &=\tfrac{1}{4}x^3+\tfrac{3}{4}x^2-\tfrac{3}{2}x-2 \end{align} "></span> The roots are 2, -1, and -4. </p> |
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