The solution of x for which the following quadratic equation holds 6×2-17ix-12=0 are

# The solution of x for which the following quadratic equation holds $6{x}^{2}-17\mathit{ix}-12=0$ are

1. A
and $\frac{3i}{2}$
2. B
and $\frac{3i}{2}$
3. C
and $\frac{2i}{3}$
4. D
and - $\frac{3i}{2}$

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### Solution:

$6{x}^{2}-17\mathit{ix}-12=0$ $6{x}^{2}9\mathit{ix}-8\mathit{ix}-12=0$ 3x(2x – 3i) – 4(2ix + 3) = 0
3x(2x – 3i) – 4( 2ix - 3${i}^{2}\right)=0$    (since,
3x(2x – 3i) – 4i(2x - 3i) = 0
(3x – 4i) (2x – 3i) = 0
3x – 4i = 0 and 2x – 3i = 0
x = and x = $\frac{3i}{2}$, which are the required solutions

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