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InterviewSolution
| 1. |
2x^2 +x+4=0 solve it completing sqaure method |
| Answer» We have{tex}2x^2 + x - 4 = 0{/tex}{tex}4x^2\xa0+ 2x - 8 = 0{/tex} [multiplying both sides by 2]{tex}4x^2 + 2x = 8{/tex}{tex}\\Rightarrow ( 2 x ) ^ { 2 } + 2 \\times 2 x \\times \\frac { 1 } { 2 } + \\left( \\frac { 1 } { 2 } \\right) ^ { 2 } = 8 + \\left( \\frac { 1 } { 2 } \\right) ^ { 2 }{/tex}\xa0[adding\xa0{tex}\\left( \\frac { 1 } { 2 } \\right) ^ { 2 }{/tex} on both sides]{tex}\\Rightarrow \\left( 2 x + \\frac { 1 } { 2 } \\right) ^ { 2 } = \\left( 8 + \\frac { 1 } { 4 } \\right) = \\frac { 33 } { 4 } = \\left( \\frac { \\sqrt { 33 } } { 2 } \\right) ^ { 2 }{/tex}{tex}\\Rightarrow{/tex}\xa02x +\xa0{tex}\\frac{1}{2} = \\pm \\left( \\frac { \\sqrt { 33 } } { 2 } \\right){/tex}\xa0[taking square root on both sides]{tex}\\Rightarrow{/tex}\xa0{tex}2x +{/tex}\xa0{tex}\\frac { 1 } { 2 } = \\frac { \\sqrt { 33 } } { 2 }{/tex}\xa0or 2x +\xa0{tex}\\frac { 1 } { 2 } = \\frac {- \\sqrt { 33 } } { 2 }{/tex}{tex}\\Rightarrow 2x=\\frac{\\sqrt{33}}{2}-\\frac{1}{2}\\ or \\ 2x=-\\frac{\\sqrt{33}}{2}-\\frac{1}{2}{/tex}{tex}\\Rightarrow x=\\frac{\\sqrt{33}-1}{4}\\ \\ or \\ \\ x=\\frac{-(\\sqrt{33}+1)}{4}{/tex} | |