(A) The given quadratic equation is $x^{2}+3x+9=0$. On comparing the given equation with $ax^{2}+bx+c=0$,we obtain $a=1, b=3,$ and $c=9$. The discrimi

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$\frac{-3 \pm 3 \sqrt{3} i}{2}$

(A) The given quadratic equation is $x^{2}+3x+9=0$. On comparing the given equation with $ax^{2}+bx+c=0$,we obtain $a=1, b=3,$ and $c=9$. The discriminant $D$ is given by $D = b^{2}-4ac$. $D = 3^{2}-4(1)(9) = 9-36 = -27$. The roots are given by the quadratic formula $x = \frac{-b \pm \sqrt{D}}{2a}$. $x = \frac{-3 \pm \sqrt{-27}}{2(1)} = \frac{-3 \pm \sqrt{27}i}{2} = \frac{-3 \pm 3\sqrt{3}i}{2}$.

Class 11 Mathematics 2 Complex Numbers and Quadratic Equations: Quadratic Equations Solution of quadratic equations and Nature of roots

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Solve the equation $x^{2}+3x+9=0$.

A
$\frac{-3 \pm 3 \sqrt{3} i}{2}$
B
$\frac{-3 \pm \sqrt{3} i}{2}$
C
$\frac{3 \pm 3 \sqrt{3} i}{2}$
D
$\frac{-3 \pm \sqrt{3}}{2}$

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2 Complex Numbers and Quadratic Equations: Quadratic Equations

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Solution of quadratic equations and Nature of roots

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