Solve the equation $2 x^{2} + x + 1 = 0$

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Solution

Step $1 :$ Given $2 x^{2} + x + 1 = 0$

Step 2: Check nature of roots
$D = b^{2} - 4 a c$
$a = 2, b = 1, c = 1$
$\Rightarrow D = 1 - 8 = - 7 < 0$
$∴ D$ is Negative.
$∴$ Roots are imaginary, so we can use the quadratic formula.

Step 3: Using quadratic formula.
$x = \frac{- b \pm \sqrt{(b^{2} - 4 a c}}{2 a}$
By putting the values of $a, b, c$
$x = \frac{- 1 \pm \sqrt{1 - 8}}{4}$
$\Rightarrow x = \frac{- 1 \pm \sqrt{- 7}}{4} \Rightarrow x = \frac{- 1 \pm \sqrt{- 7} i}{4}$ $∵ \sqrt{- 1} = i$

The values of $x$ are $\frac{- 1 + \sqrt{7} i}{4}, \frac{- 1 - \sqrt{7} i}{4}$

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