(A) The given quadratic equation is $\sqrt{2} x^{2} + x + \sqrt{2} = 0$. On comparing the given equation with $ax^{2} + bx + c = 0$,we obtain $a = \sq

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$\frac{-1 \pm \sqrt{7} i}{2 \sqrt{2}}$

(A) The given quadratic equation is $\sqrt{2} x^{2} + x + \sqrt{2} = 0$. On comparing the given equation with $ax^{2} + bx + c = 0$,we obtain $a = \sqrt{2}$,$b = 1$,and $c = \sqrt{2}$. The discriminant $D$ is given by $D = b^{2} - 4ac$. $D = (1)^{2} - 4(\sqrt{2})(\sqrt{2}) = 1 - 8 = -7$. The roots are given by the quadratic formula $x = \frac{-b \pm \sqrt{D}}{2a}$. $x = \frac{-1 \pm \sqrt{-7}}{2(\sqrt{2})} = \frac{-1 \pm \sqrt{7}i}{2\sqrt{2}}$.

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

Medium

Solve the equation $\sqrt{2} x^{2} + x + \sqrt{2} = 0$.

A
$\frac{-1 \pm \sqrt{7} i}{2 \sqrt{2}}$
B
$\frac{-1 \pm \sqrt{5} i}{2 \sqrt{2}}$
C
$\frac{-1 \pm \sqrt{3} i}{2 \sqrt{2}}$
D
$\frac{-1 \pm \sqrt{9} i}{2 \sqrt{2}}$

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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 $\sqrt{2} x^{2} + x + \sqrt{2} = 0$.

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Suppose $a, b, c$ are real numbers,and each of the equations $x^2+2ax+b^2=0$ and $x^2+2bx+c^2=0$ has two distinct real roots. Then,the equation $x^2+2cx+a^2=0$ has

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