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Let $x_{1}, x_{2}, \ldots \ldots, x_{6}$ be the roots of the polynomial equation
$\mathrm{x}^{6}+2 \mathrm{x}^{5}+4 \mathrm{x}^{4}+8 \mathrm{x}^{3}+16 \mathrm{x}^{2}+32 \mathrm{x}+64=0$
Then
Options:
$\mathrm{x}^{6}+2 \mathrm{x}^{5}+4 \mathrm{x}^{4}+8 \mathrm{x}^{3}+16 \mathrm{x}^{2}+32 \mathrm{x}+64=0$
Then
Solution:
1238 Upvotes
Verified Answer
The correct answer is:
$\left|\mathrm{x}_{\mathrm{i}}\right|=2$ for all values of i
It form an G.P.
$\frac{x^{6}\left(1-\left(\frac{2}{x}\right)^{7}\right)}{\left(1-\frac{2}{x}\right)}=0$
solve that
$\begin{array}{l}
x^{7}=2^{7} \\
x=2
\end{array}$
$\frac{x^{6}\left(1-\left(\frac{2}{x}\right)^{7}\right)}{\left(1-\frac{2}{x}\right)}=0$
solve that
$\begin{array}{l}
x^{7}=2^{7} \\
x=2
\end{array}$
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