Browse by Stream
QnA
Home
Search for Exam, Articles, Questions
QnA
get app
Go To Your Study Dashboard
  1. Home
  2. Need explanation for: - Complex numbers and quadratic equations - JEE Main-7
# Engineering

If \alpha and \beta are the roots of the quadratic equation,

x^{2}+xsin\theta -2sin\theta =0,\theta \epsilon (0,\frac{\pi}{2}), then 

\frac{\alpha ^{12}+\beta ^{12}}{(\alpha ^{-12}+\beta ^{-12})\cdot (\alpha -\beta )^{24}} is equal to :

  • Option 1)

    \frac{2^{12}}{(sin\theta-4)^{12}}

  • Option 2)

    \frac{2^{12}}{(sin\theta+8)^{12}}

  • Option 3)

    \frac{2^{12}}{(sin\theta-8)^{6}}

  • Option 4)

    \frac{2^{6}}{(sin\theta+8)^{12}}

 

Answers (1)
V Vakul

\alpha and \beta are the roots of the equation 

x^{2}+xsin\theta -2sin\theta =0

\alpha +\beta =-sin\theta

\alpha \beta =-2sin\theta

Now,

\frac{\alpha ^{12}+\beta ^{12}}{(\alpha ^{-12}+\beta ^{-12})\cdot (\alpha -\beta )^{24}}=\frac{(\alpha\beta)^{12}}{(\alpha-\beta)^{24}}

                                                   =\frac{(\alpha \beta )^{12}}{[(\alpha +\beta )^{2}-4\alpha \beta ]^{12}}

                                                      =[\frac{-2sin\theta}{sin^{2}\theta+8sin\theta}]^{12}

                                                      =\frac{2^{12}}{(sin\theta+8)^{12}}

correct option (2)


Option 1)

\frac{2^{12}}{(sin\theta-4)^{12}}

Option 2)

\frac{2^{12}}{(sin\theta+8)^{12}}

Option 3)

\frac{2^{12}}{(sin\theta-8)^{6}}

Option 4)

\frac{2^{6}}{(sin\theta+8)^{12}}

Similar Questions

Preparation Products

Knockout JEE Main April 2021 (One Month)

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 14000/- ₹ 6999/-
Buy Now
Knockout JEE Main April 2021

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 22999/- ₹ 14999/-
Buy Now
Test Series JEE Main April 2021

Take chapter-wise, subject-wise and Complete syllabus mock tests and get in depth analysis of your test..

₹ 6999/- ₹ 4999/-
Buy Now
Knockout JEE Main April 2022

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 34999/- ₹ 24999/-
Buy Now
JEE Main Rank Booster 2021

This course will help student to be better prepared and study in the right direction for JEE Main..

₹ 13999/- ₹ 9999/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
Start Now
 
Exams
Articles
Questions