Question:
$x^{2}+3 i x+10=0$
Solution:
Given:
$x^{2}+3 i x+10=0$
$\Rightarrow \mathrm{x}^{2}+5 \mathrm{ix}-2 \mathrm{i} \mathrm{x}+10=0$
$\Rightarrow x(x+5 i)-2 i\left(x-\frac{10}{2 i}\right)=0$
$\Rightarrow x(x+5 i)-2 i\left(x-\frac{5 \times i}{i \times i}\right)=0$
$\Rightarrow^{x(x+5 i)-2 i\left(x-\frac{5 \times i}{-1}\right)}=0$
$\Rightarrow x(x+5 i)-2 i(x+5 i)=0$
$\Rightarrow(x+5 i)(x-2 i)=0$
$\Rightarrow \mathrm{x}+5 \mathrm{i}=0 \& \mathrm{x}-2 \mathrm{i}=0$
$\Rightarrow \mathrm{x}=-5 \mathrm{i} \& \mathrm{x}=2 \mathrm{i}$
Ans: $x=-5 i \& x=2 i$
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