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By using the method of completing the square show that the equation 2x2+x+4=0 has no real roots |
| Answer» We have, 2x2 + x + 4 = 0Dividing both sides by 2, we get{tex}x^2 +{1 \\over 2}x + 2 = 0 {/tex}{tex}\\implies (x)^2 + {1 \\over 2}x + {1 \\over 16} = -2 + {1 \\over 16}{/tex}{tex}\\implies (x)^2 + 2(x) ({1 \\over 4})+ ({1 \\over4})^2= {- 32 +1 \\over 16}{/tex}{tex}\\implies (x + {1 \\over4})^2 = -{31 \\over 16} <0{/tex}Which is not possible, as square cannot be negative.So, there is no real value of x which satisfy the given equation.Therefore, the given equation has no real roots. | |