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

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

A
$\frac{-1 \pm \sqrt{7}i}{4}$
B
$\frac{-1 \pm \sqrt{5}i}{4}$
C
$\frac{-1 \pm \sqrt{3}i}{4}$
D
$\frac{-1 \pm \sqrt{2}i}{4}$

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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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