The distance of the roots of the equation _ n z^ n + _ 1 z^ n-1 + + _ n =3 from origin…
Mathematics · JEE Main · NTA Exams — Complex Numbers and Quadratic Equations
The distance of the roots of the equation \(\tan \theta_{n} z^{n}+\tan \theta_{1} z^{n-1}+\ldots+\tan \theta_{n}=3\) from origin, where \(\theta_{n}, \theta_{1}, \theta_{2}, \ldots, \theta_{n} \in\left[0, \frac{\pi}{4}\right]\) satisfy
- greater than 2/3
- less than 2/3
- greater than \(\left|\cos \theta_{1}\right|+\left|\cos \theta_{2}\right|+\ldots+\left|\cos \theta_{n}\right|\)
- less than \(\left|\cos \theta_{1}\right|+\left|\cos \theta_{2}\right|+\ldots+\left|\cos \theta_{n}\right|\)
Answer
(B) less than 2/3
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