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

$(a)\;\large\frac{-1 \pm \sqrt{7} i}{-3}\qquad(b)\;\large\frac{-1 \pm \sqrt{3} i}{-2}\qquad(c)\;\large\frac{-1 \pm \sqrt{5} i}{-2}\qquad(d)\;\large\frac{1 \pm \sqrt{7} i}{2}$

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Answer : $\;\large\frac{1 \pm \sqrt{7} i}{2}$
Explanation :
The given quadratic equation is $\;x^2-x+2=0$
On comparing the given equation with $\;ax^2 + bx +c\;,$ we obtain
$a=1\;,b=-1\;and \;c=2$
Therefore , the discriminant of the given equation is
$D = b^2 -4ac=(-1)^{2} - 4 \times (1) \times (2) =-7$
Therefore , the required solutions are
$\large\frac{-b \pm D}{2a} = -\large\frac{-(-1) \pm \sqrt{-7}}{2 \times 1}$
$=\large\frac{1 \pm \sqrt{7} i}{2} \qquad [\sqrt{-1} = i]$
answered Apr 11, 2014 by yamini.v
 
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