Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
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
MathematicsSequences and SeriesKVPYKVPY 2017 (19 Nov SB/SX)
Options:
  • A $\left|\mathrm{x}_{\mathrm{i}}\right|=2$ for exactly one value of $\mathrm{i}$
  • B $\left|x_{i}\right|=2$ for exactly two values of $i$
  • C $\left|\mathrm{x}_{\mathrm{i}}\right|=2$ for all values of i
  • D $\left|\mathrm{x}_{\mathrm{i}}\right|=2$ for no value of $\mathrm{i}$
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
$\begin{array}{l}
x^{7}=2^{7} \\
x=2
\end{array}$

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.