Solve the following quadratic equations. 2 x^2+3 ix+2=0 - Vidyadip

Question

Solve the following quadratic equations.
$2 \mathrm{x}^2+3 \mathrm{ix}+2=0$

✓

Answer

$2 \mathrm{x}^2+3 \mathrm{ix}+2=0$
Solution:
Given equation is $2 x^2+3 i x+2=0$
Comparing with $a x^2+b x+c=0$, we get
$
a=2, b=3 i, c=2
$
Discriminant $=b^2-4 a c$
$
\begin{aligned}
& =(3 i)^2-4 \times 2 \times 2 \\
& =9 i^2-16 \\
& =-9-16 \\
& =-25<0
\end{aligned}
$
So, the given equation has complex roots.
These roots are given by
$
\begin{aligned}
x & =\frac{-\mathrm{b} \pm \sqrt{\mathrm{b}^2-4 a \mathrm{a}}}{2 \mathrm{a}} \\
& =\frac{-3 \mathrm{i} \pm \sqrt{-25}}{2(2)} \\
x & =\frac{-3 \mathrm{i} \pm 5 \mathrm{i}}{4} \\
x & =\frac{-3 \mathrm{i}+5 \mathrm{i}}{4} \text { or } x=\frac{-3 \mathrm{i}-5 \mathrm{i}}{4} \\
x & =\frac{1}{2} \mathrm{i} \text { } x=-2 \mathrm{i}
\end{aligned}
$
$\therefore$ the roots of the given equation are $\frac{1}{2} \mathrm{i}$ and $-2 \mathrm{i}$.

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