Solve the following quadratic equations. i x^2-4 x-4 i=0 - Vidyadip

Question

Solve the following quadratic equations.
$i x^2-4 x-4 i=0$

✓

Answer

$
i x^2-4 x-4 i=0
$
Multiplying throughout by $\mathrm{i}$, we get
$
\begin{aligned}
& \mathrm{i}^2 \mathrm{x}^2-4 \mathrm{ix}-4 \mathrm{i}^2=0 \\
& \therefore-\mathrm{x}^2-4 \mathrm{ix}+4=0 \ldots \ldots\left[\because \mathrm{i}^2=-1\right] \\
& \therefore \mathrm{x}^2+4 \mathrm{ix}-4=0
\end{aligned}
$
Comparing with $a x^2+b x+c=0$, we get
$
a=1, b=4 i, c=-4
$
Discriminant $=b^2-4 a c$
$
\begin{aligned}
& =(4 i)^2-4 \times 1 \times-4 \\
& =16 i^2+16 \\
& =-16+16 \ldots . .\left[\because i^2=-1\right] \\
& =0
\end{aligned}
$
So, the given equation has equal roots.
These roots are given by
$
\begin{aligned}
x & =\frac{-\mathrm{b} \pm \sqrt{\mathrm{b}^2-4 \mathrm{ac}}}{2 \mathrm{a}} \\
& =\frac{-4 \mathrm{i} \pm \sqrt{0}}{2(1)}=\frac{-4 \mathrm{i}}{2}
\end{aligned}
$
$x=-2 \mathrm{i}$
$\therefore$ the roots of the given equation are $-2 \mathrm{i}$ and $-2 \mathrm{i}$.

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