Solve the following quadratic equation :

$i x^{2} - x + 12 i = 0$

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Solution

We have, $i x^{2} - x + 12 i = 0$

$\Rightarrow x^{2} - \frac{1}{i} x + 12 = 0$

$\Rightarrow x^{2} + i x + 12 = 0 [∵ i = - \frac{1}{i}]$

On comparing with general form of quadratic
equation $a x^{2} + b x + c = 0$

We get $a = 1, b = i, c = 12$

Roots of the equation are

$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

$= \frac{- i \pm \sqrt{i^{2} - 4 \times 1 \times 12}}{2}$

$x = \frac{- i \pm \sqrt{- 1 - 48}}{2} = \frac{- i \pm \sqrt{- 49}}{2}$

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

$= \frac{- i + 7 i}{2} = \frac{- i - 7 i}{2}$

$\frac{6 i}{2}, \frac{- 8 i}{2}$

$= 3 i, - 4 i$

Hence, the roots are $- 4 i$ and $3 i$

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$(x - 4) (x + 2) = 0$

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