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

Question

Solve the following quadratic equations.
$\mathrm{x}^2+4 \mathrm{ix}-4=0$

✓

Answer

Given equation is $x^2+4 i x-4=0$
Comparing with $a x^2+b x+c=0$, we get
$
\begin{aligned}
& a=1, b=4 i, c=-4 \\
& \text { Discriminant }=b^2-4 a c \\
& =(4 i)^2-4 \times 1 \times-4 \\
& =16 i^2+16 \\
& \left.=-16+16 \ldots . . \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} \text { }} \\
& =\frac{-4 \mathrm{i} \pm \sqrt{0}}{2(1)}=\frac{-4 \mathrm{i}}{2} \\
x & =-2 \mathrm{i}
\end{aligned}
$
$\therefore$ the roots of the given equation are $-2 \mathrm{i}$ and $-2 \mathrm{i}$.

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