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1. x2 + 4x + 3 = 02. x2 - 5x + 4 = 03. x2 + 7 = 0 |
| Answer» <html><body><p></p><p><img align="absmiddle" alt="(i) \: {x}^{2} + 4x + 3 = <klux>0</klux> \\ {x}^{2} + x + 3x + 3 = 0 \\ x(x + 1) + 3(x + 1) = 0 \\ (x + 1)(x + 3) = 0 \\ x = - 1, - 3" class="latex-formula" id="TexFormula1" src="https://tex.z-dn.net/?f=%28i%29%20%5C%3A%20%20%7Bx%7D%5E%7B2%7D%20%20%2B%204x%20%2B%203%20%3D%200%20%5C%5C%20%20%7Bx%7D%5E%7B2%7D%20%20%2B%20x%20%2B%203x%20%2B%203%20%3D%200%20%5C%5C%20x%28x%20%2B%201%29%20%2B%203%28x%20%2B%201%29%20%3D%200%20%5C%5C%20%28x%20%2B%201%29%28x%20%2B%203%29%20%3D%200%20%5C%5C%20x%20%3D%20%20-%201%2C%20-%203" title="(i) \: {x}^{2} + 4x + 3 = 0 \\ {x}^{2} + x + 3x + 3 = 0 \\ x(x + 1) + 3(x + 1) = 0 \\ (x + 1)(x + 3) = 0 \\ x = - 1, - 3"/></p><p><img align="absmiddle" alt="(ii) \: {x}^{2} - 5x + 4 \\ {x}^{2} - x - 4x + 4 = 0 \\ x(x - 1) - 4(x - 1) = 0 \\ (x - 1)(x - 4) = 0 \\ x = 1,4" class="latex-formula" id="TexFormula2" src="https://tex.z-dn.net/?f=%28ii%29%20%5C%3A%20%20%7Bx%7D%5E%7B2%7D%20%20-%205x%20%2B%204%20%5C%5C%20%20%7Bx%7D%5E%7B2%7D%20%20-%20x%20%20-%204x%20%2B%204%20%3D%200%20%5C%5C%20x%28x%20-%201%29%20-%204%28x%20-%201%29%20%3D%200%20%5C%5C%20%28x%20-%201%29%28x%20-%204%29%20%3D%200%20%5C%5C%20x%20%3D%201%2C4" title="(ii) \: {x}^{2} - 5x + 4 \\ {x}^{2} - x - 4x + 4 = 0 \\ x(x - 1) - 4(x - 1) = 0 \\ (x - 1)(x - 4) = 0 \\ x = 1,4"/></p><p>(iii) <a href="https://interviewquestions.tuteehub.com/tag/solve-647535" style="font-weight:bold;" target="_blank" title="Click to know more about SOLVE">SOLVE</a> : x2+7 = 0 </p><p></p><p> Subtract 7 from both <a href="https://interviewquestions.tuteehub.com/tag/sides-1207029" style="font-weight:bold;" target="_blank" title="Click to know more about SIDES">SIDES</a> of the equation : </p><p> x2 = -7</p><p> </p><p> When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get: </p><p> x = ± √ -7 </p><p></p><p> In Math, i is called the imaginary <a href="https://interviewquestions.tuteehub.com/tag/unit-1438166" style="font-weight:bold;" target="_blank" title="Click to know more about UNIT">UNIT</a>. It satisfies i2 =-1. Both i and -i are the square roots of -1 </p><p></p><p>Accordingly, √ -7 =</p><p> √ -1• 7 =</p><p> √ -1 •√ 7 =</p><p> i • √ 7</p><p></p><p>The equation has no <a href="https://interviewquestions.tuteehub.com/tag/real-1178490" style="font-weight:bold;" target="_blank" title="Click to know more about REAL">REAL</a> solutions. It has 2 imaginary, or complex solutions.</p><p></p><p> x= 0.0000 + 2.6458 i </p><p> x= 0.0000 - 2.6458 i </p></body></html> | |