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Solve the equation : $\;2x^{2}+x+1=0\;$

$(a)\;\large\frac{-1\pm \sqrt{3} i}{4}\qquad(b)\;\large\frac{-1\pm \sqrt{5} i}{7}\qquad(c)\;\large\frac{-1\pm \sqrt{5} i}{4}\qquad(d)\;\large\frac{-1\pm \sqrt{7} i}{4}$

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Answer : $\;\large\frac{-1\pm \sqrt{7} i}{4}$
Explanation :
The given quadratic equation is $\;2x^2+x+1=0$
On comparing the given equation with $\;ax^2 + bx +c\;,$ we obtain
$a=2\;,b=1\;and \;c=1$
Therefore , the discriminant of the given equation is
$D = b^2 -4ac=1^{2} - 4 \times 2 \times 1 =-7$
Therefore , the required solutions are
$\large\frac{-b \pm D}{2a} = -\large\frac{-1 \pm \sqrt{-7}}{2 \times 2}$
$=\large\frac{-1\pm \sqrt{7} i}{4} \qquad [\sqrt{-1} =i]$
answered Apr 10, 2014 by yamini.v
 
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