Solve the following quadratic equations. 8 x^2+2 x+1=0 - Vidyadip

Question

Solve the following quadratic equations.
$8 x^2+2 x+1=0$

✓

Answer

Given equation is $8 x^2+2 x+1=0$
Comparing with $a x^2+b x+c=0$, we get
$
\begin{aligned}
& a=8, b=2, c=1 \\
& \text { Discriminant }=b^2-4 a c \\
& =(2)^2-4 \times 8 \times 1 \\
& =4-32 \\
& =-28<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 \mathrm{ac}}}{2 \mathrm{a}} \\
& =\frac{-2 \pm \sqrt{-28}}{2(8)} \\
& =\frac{-2 \pm 2 \sqrt{7} \mathrm{i}}{16 \text { }} \\
x & =\frac{-1 \pm \sqrt{7} \mathrm{i}}{8}
\end{aligned}
$
$\therefore$ the roots of the given equation are $\frac{-1+\sqrt{7 \mathrm{i}}}{8}$ and $\frac{-1-\sqrt{7 \mathrm{i}}}{8}$

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