(A) The given quadratic equation is $x^{2}+3x+5=0$. Comparing this with the standard form $ax^{2}+bx+c=0$,we get $a=1, b=3, c=5$. The discriminant $D$

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(A) The given quadratic equation is $x^{2}+3x+5=0$. Comparing this with the standard form $ax^{2}+bx+c=0$,we get $a=1, b=3, c=5$. The discriminant $D$ is given by $D = b^{2}-4ac$. $D = 3^{2}-4(1)(5) = 9-20 = -11$. The roots are given by the quadratic formula $x = \frac{-b \pm \sqrt{D}}{2a}$. $x = \frac{-3 \pm \sqrt{-11}}{2(1)} = \frac{-3 \pm \sqrt{11}i}{2}$ (since $\sqrt{-1} = i$).

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

Medium

Solve the equation $x^{2}+3x+5=0$.

A
$\frac{-3 \pm \sqrt{11}i}{2}$
B
$\frac{-3 \pm \sqrt{13}i}{2}$
C
$\frac{-3 \pm \sqrt{15}i}{2}$
D
$\frac{-3 \pm \sqrt{17}i}{2}$

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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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Solve the equation $x^{2}+3x+5=0$.

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