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Solve the equation : $\;x^{2}+3=0\;$

$(a)\;\pm 3 i\qquad(b)\;\pm 2i\qquad(c)\;\pm \sqrt{2} i\qquad(d)\;\pm \sqrt{3} i$

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Answer : $\;\pm \sqrt{3} i$
Explanation :
The given quadratic equation is $\;x^2+3=0$
On comparing the given equation with $\;ax^2 + bx +c\;,$ we obtain
$a=1\;,b=0\;and \;c=3$
Therefore , the discriminant of the given equation is
$D = b^2 -4ac=0^{2} - 4 \times 1 \times 3 =-12$
Therefore , the required solutions are
$\large\frac{-b \pm D}{2a} = -\large\frac{\sqrt{-12}}{2 \times 1}$
$ = \large\frac{\pm \sqrt{12}i}{2} \qquad [\sqrt{-1} =i]$
$= \pm \large\frac{2 \sqrt{3}i}{2} = \pm \sqrt{3} i$
answered Apr 10, 2014 by yamini.v
 
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