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Solve the equation : $\;x^{2}+3x+5=0\;$

$(a)\;\large\frac{-3\pm \sqrt{11} i}{2}\qquad(b)\;\large\frac{-3\pm \sqrt{7} i}{2}\qquad(c)\;\large\frac{-3\pm \sqrt{5} i}{2}\qquad(d)\;\large\frac{\pm \sqrt{11} i}{2}$

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Answer : $\;\large\frac{-3\pm \sqrt{11} i}{2}$
Explanation :
The given quadratic equation is $\;x^2+3x+5=0$
On comparing the given equation with $\;ax^2 + bx +c\;,$ we obtain
$a=1\;,b=3\;and \;c=5$
Therefore , the discriminant of the given equation is
$D = b^2 -4ac=3^{2} - 4 \times (1) \times (5) =-11$
Therefore , the required solutions are
$\large\frac{-b \pm D}{2a} = -\large\frac{-3 \pm \sqrt{-11}}{2 \times (1)}$
$=\large\frac{-3\pm \sqrt{11} i}{2} \qquad [\sqrt{-1} =i]$
answered Apr 11, 2014 by yamini.v
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