JEE Exam > JEE Questions > If the roots of the equation 1/ x + p + 1/ ...
Start Learning for Free
If the roots of the equation 1/ x + p + 1/ x + q = 1/r are equal in magnitude but opposite in sign, then (p + q) equals
- a)2r
- b)r
- c)- 2r
- d)none of htese
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If the roots of the equation 1/ x + p + 1/ x + q = 1/r are equal in ...
Free Test
FREE
| Start Free Test |
Community Answer
If the roots of the equation 1/ x + p + 1/ x + q = 1/r are equal in ...
Given:
The equation is 1/xp * 1/xq = 1/r, where p and q are constants and r is a variable.
To find:
The value of (p+q).
Solution:
Step 1: Simplify the equation:
1/xp * 1/xq = 1/r
Multiplying both sides by xp * xq * r:
r = xp * xq
Step 2: Analyzing the roots:
Let's assume the roots of the equation are a and -a, where a is a non-zero real number.
Case 1: a is positive
If a is positive, then the roots of the equation are a and -a, where both a and -a are positive. In this case, we can write the equation as:
r = a * (-a) = -a^2
Case 2: a is negative
If a is negative, then the roots of the equation are -a and a, where both -a and a are negative. In this case, we can write the equation as:
r = (-a) * a = -a^2
Step 3: Comparing the equations:
From both cases, we can see that the value of r is the same, which means:
-a^2 = -a^2
Step 4: Comparing the coefficients:
Comparing the coefficients of both equations, we get:
xp * xq = (-a)^2
Step 5: Equating the coefficients:
Comparing the coefficients of both equations, we get:
xp * xq = a^2
Step 6: Comparing the exponents:
Since the bases are the same (x), the exponents must be equal:
p + q = 2
Step 7: Conclusion:
Therefore, the value of (p + q) is 2, which corresponds to option 'A'.
The equation is 1/xp * 1/xq = 1/r, where p and q are constants and r is a variable.
To find:
The value of (p+q).
Solution:
Step 1: Simplify the equation:
1/xp * 1/xq = 1/r
Multiplying both sides by xp * xq * r:
r = xp * xq
Step 2: Analyzing the roots:
Let's assume the roots of the equation are a and -a, where a is a non-zero real number.
Case 1: a is positive
If a is positive, then the roots of the equation are a and -a, where both a and -a are positive. In this case, we can write the equation as:
r = a * (-a) = -a^2
Case 2: a is negative
If a is negative, then the roots of the equation are -a and a, where both -a and a are negative. In this case, we can write the equation as:
r = (-a) * a = -a^2
Step 3: Comparing the equations:
From both cases, we can see that the value of r is the same, which means:
-a^2 = -a^2
Step 4: Comparing the coefficients:
Comparing the coefficients of both equations, we get:
xp * xq = (-a)^2
Step 5: Equating the coefficients:
Comparing the coefficients of both equations, we get:
xp * xq = a^2
Step 6: Comparing the exponents:
Since the bases are the same (x), the exponents must be equal:
p + q = 2
Step 7: Conclusion:
Therefore, the value of (p + q) is 2, which corresponds to option 'A'.
|
Explore Courses for JEE exam
|
|
Top Courses for JEEView all
If the roots of the equation 1/ x + p + 1/ x + q = 1/r are equal in magnitude but opposite in sign, then (p + q) equalsa)2rb)rc)- 2rd)none of hteseCorrect answer is option 'A'. Can you explain this answer?
Question Description
If the roots of the equation 1/ x + p + 1/ x + q = 1/r are equal in magnitude but opposite in sign, then (p + q) equalsa)2rb)rc)- 2rd)none of hteseCorrect answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If the roots of the equation 1/ x + p + 1/ x + q = 1/r are equal in magnitude but opposite in sign, then (p + q) equalsa)2rb)rc)- 2rd)none of hteseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the roots of the equation 1/ x + p + 1/ x + q = 1/r are equal in magnitude but opposite in sign, then (p + q) equalsa)2rb)rc)- 2rd)none of hteseCorrect answer is option 'A'. Can you explain this answer?.
If the roots of the equation 1/ x + p + 1/ x + q = 1/r are equal in magnitude but opposite in sign, then (p + q) equalsa)2rb)rc)- 2rd)none of hteseCorrect answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If the roots of the equation 1/ x + p + 1/ x + q = 1/r are equal in magnitude but opposite in sign, then (p + q) equalsa)2rb)rc)- 2rd)none of hteseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the roots of the equation 1/ x + p + 1/ x + q = 1/r are equal in magnitude but opposite in sign, then (p + q) equalsa)2rb)rc)- 2rd)none of hteseCorrect answer is option 'A'. Can you explain this answer?.
Solutions for If the roots of the equation 1/ x + p + 1/ x + q = 1/r are equal in magnitude but opposite in sign, then (p + q) equalsa)2rb)rc)- 2rd)none of hteseCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of If the roots of the equation 1/ x + p + 1/ x + q = 1/r are equal in magnitude but opposite in sign, then (p + q) equalsa)2rb)rc)- 2rd)none of hteseCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If the roots of the equation 1/ x + p + 1/ x + q = 1/r are equal in magnitude but opposite in sign, then (p + q) equalsa)2rb)rc)- 2rd)none of hteseCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for If the roots of the equation 1/ x + p + 1/ x + q = 1/r are equal in magnitude but opposite in sign, then (p + q) equalsa)2rb)rc)- 2rd)none of hteseCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of If the roots of the equation 1/ x + p + 1/ x + q = 1/r are equal in magnitude but opposite in sign, then (p + q) equalsa)2rb)rc)- 2rd)none of hteseCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If the roots of the equation 1/ x + p + 1/ x + q = 1/r are equal in magnitude but opposite in sign, then (p + q) equalsa)2rb)rc)- 2rd)none of hteseCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup