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Solve the equation : $\;x^{2}+3x+9=0\;$

$(a)\;\large\frac{-5 \pm3 \sqrt{3}i}{2}\qquad(b)\;\large\frac{3 \pm3 \sqrt{3}i}{2}\qquad(c)\;\large\frac{-3 \pm 3 \sqrt{3}i}{2}\qquad(d)\;0$

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Answer : $\;\large\frac{-3 \pm 3 \sqrt{3}i}{2}$
Explanation :
The given quadratic equation is $\;x^2+3x+9=0$
On comparing the given equation with $\;ax^2 + bx +c\;,$ we obtain
$a=1\;,b=3\;and \;c=9$
Therefore , the discriminant of the given equation is
$D = b^2 -4ac=3^{2} - 4 \times 1 \times 9 =-7$
Therefore , the required solutions are
$\large\frac{-b \pm D}{2a} = -\large\frac{-3 \pm \sqrt{-27}}{2(1)}$
$= \large\frac{-3 \pm 3 \sqrt{-3} }{2}$
$=\large\frac{-3 \pm 3 \sqrt{3}i}{2} \qquad [\sqrt{-1} =1]$
answered Apr 11, 2014 by yamini.v
 
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