The number of real roots of the equation 

5+|2^{x}-1|=2^{x}(2^{x}-2) is : 

  • Option 1)

    3

  • Option 2)

    2

  • Option 3)

    4

  • Option 4)

    1

 

Answers (1)
V Vakul

5+|2^{x}-1|=2^{x}(2^{x}-2)

5+|2^{x}-1|=2^{2x}-2\cdot 2^{x}

Case 1: x\geq 0

=>5+2^{x}-1=2^{2x}-2\cdot 2^{x}

=>2^{2x}-2\cdot 2^{x}-2^{x}-4=0

=>(2^{x}-4)(2^{x}+1)=0

=>2^{x}-4=0

=>x=2

Case 2: x< 0

5+1-2^{x}=2^{2x}-2\cdot 2^{x}

=>6=2^{2x}- 2^{x}

LHS = +ve  &  RHS = - ve (no solution)

\therefore no. of solution = 1

option(4) will be correct answer.


Option 1)

3

Option 2)

2

Option 3)

4

Option 4)

1

Preparation Products

Knockout JEE Main April 2021

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

₹ 22999/- ₹ 14999/-
Buy Now
Knockout JEE Main April 2022

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

₹ 34999/- ₹ 24999/-
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
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
Test Series JEE Main April 2022

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

₹ 6999/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
 
Exams
Articles
Questions