Bài 4: Công thức nghiệm của phương trình bậc hai
Hướng dẫn giải Bài 15 (Trang 45 SGK Toán Đại số 9, Tập 2)
<p>Kh&ocirc;ng giải phương tr&igrave;nh, h&atilde;y x&aacute;c định c&aacute;c hệ số a, b, c, t&iacute;nh biệt thức&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#8710;</mo></math> v&agrave; x&aacute;c định số nghiệm của mỗi phương tr&igrave;nh sau :</p> <p>a)&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><msup><mi>x</mi><mn>2</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>2</mn><mi>x</mi><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>3</mn><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>0</mn><mo>&#160;</mo><mo>;</mo></math>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;b)&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><msup><mi>x</mi><mn>2</mn></msup><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>2</mn><msqrt><mn>10</mn></msqrt><mo>&#160;</mo><mi>x</mi><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>2</mn><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>0</mn><mo>;</mo></math></p> <p>c)<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><msup><mi>x</mi><mn>2</mn></msup><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>7</mn><mi>x</mi><mo>&#160;</mo><mo>+</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>=</mo><mo>&#160;</mo><mn>0</mn><mo>&#160;</mo><mo>;</mo></math>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; d) <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mn>7</mn><msup><mi>x</mi><mn>2</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>1</mn><mo>,</mo><mn>2</mn><mi>x</mi><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>0</mn><mo>&#160;</mo><mo>;</mo></math></p> <p><strong>Giải</strong></p> <p>a) <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><msup><mi>x</mi><mn>2</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>2</mn><mi>x</mi><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>3</mn><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>0</mn><mo>&#160;</mo><mo>&#160;</mo><mi>c</mi><mi>&#243;</mi><mo>&#160;</mo><mi>a</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>7</mn><mo>,</mo><mo>&#160;</mo><mi>b</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>&#160;</mo><mi>c</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>3</mn></math></p> <p>&nbsp; &nbsp; &nbsp; <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#8710;</mo><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msup><mfenced><mrow><mo>-</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>4</mn><mo>.</mo><mn>7</mn><mo>.</mo><mn>3</mn><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mo>-</mo><mn>80</mn><mo>:</mo></math> V&ocirc; nghiệm</p> <p>b)&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><msup><mi>x</mi><mn>2</mn></msup><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>2</mn><msqrt><mn>10</mn></msqrt><mo>&#160;</mo><mi>x</mi><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>2</mn><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>0</mn><mo>&#160;</mo><mi>c</mi><mi>&#243;</mi><mo>&#160;</mo><mi>a</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>5</mn><mo>,</mo><mo>&#160;</mo><mi>b</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>2</mn><msqrt><mn>10</mn></msqrt><mo>,</mo><mo>&#160;</mo><mi>c</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>2</mn></math></p> <p>&nbsp; &nbsp; &nbsp; &nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#8710;</mo><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msup><mfenced><mrow><mn>2</mn><msqrt><mn>10</mn></msqrt></mrow></mfenced><mn>2</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>4</mn><mo>.</mo><mn>5</mn><mo>.</mo><mn>2</mn><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>0</mn><mo>:</mo></math> Nghiệm k&eacute;p</p> <p>c)&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><msup><mi>x</mi><mn>2</mn></msup><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>7</mn><mi>x</mi><mo>&#160;</mo><mo>+</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>=</mo><mo>&#160;</mo><mn>0</mn><mo>&#160;</mo><mo>&#160;</mo><mi>c</mi><mi>&#243;</mi><mo>&#160;</mo><mi>a</mi><mo>&#160;</mo><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>;</mo><mo>&#160;</mo><mi>b</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>7</mn><mo>;</mo><mo>&#160;</mo><mi>c</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></math></p> <p>&nbsp; &nbsp; &nbsp; <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#8710;</mo><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msup><mn>7</mn><mn>2</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>4</mn><mo>.</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>.</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>49</mn><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mfrac><mn>143</mn><mn>3</mn></mfrac><mo>:</mo></math> Phương tr&igrave;nh c&oacute; hai nghiệm ph&acirc;n biệt</p> <p>d) <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mn>7</mn><msup><mi>x</mi><mn>2</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>1</mn><mo>,</mo><mn>2</mn><mi>x</mi><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>0</mn><mo>&#160;</mo><mo>&#160;</mo><mi>c</mi><mi>&#243;</mi><mo>&#160;</mo><mi>a</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>7</mn><mo>;</mo><mo>&#160;</mo><mi>b</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>;</mo><mo>&#160;</mo><mi>c</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>1</mn></math></p> <p>&nbsp; &nbsp; &nbsp; &nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#8710;</mo><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msup><mfenced><mrow><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>4</mn><mo>.</mo><mn>1</mn><mo>,</mo><mn>7</mn><mo>.</mo><mfenced><mrow><mo>-</mo><mn>2</mn><mo>,</mo><mn>1</mn></mrow></mfenced><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>1</mn><mo>,</mo><mn>44</mn><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>14</mn><mo>,</mo><mn>28</mn><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>15</mn><mo>,</mo><mn>72</mn><mo>:</mo></math> Phương tr&igrave;nh c&oacute; hai nghiệm ph&acirc;n biệt</p> <p>&nbsp;</p> <p>&nbsp;</p> <p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;</p> <p>&nbsp;</p> <p>&nbsp;</p>
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