Class 11 Exam > Class 11 Questions > consider y=2x/1+x², where x is real , then th...
Start Learning for Free
consider y=2x/1+x², where x is real , then the range of expression y²+y-2 is [a,b]. Find b - 4a. Please solve this quadratic problem
Most Upvoted Answer
consider y=2x/1+x², where x is real , then the range of expression y²+...
So b= 0 and a = -9/4 and hence b - 4a = 9
Community Answer
consider y=2x/1+x², where x is real , then the range of expression y²+...
Problem Statement: Consider y=2x/1 x², where x is real, then the range of expression y² y-2 is [a,b]. Find b - 4a.
Solution:
Step 1: Find the range of y
y=2x/1 x² = 2/x
Since x is real, we know that x can be positive, negative or zero. However, we cannot have y=0 as it would make the denominator of the expression undefined.
Therefore, the range of y is (-∞, 0) U (0, ∞)
Step 2: Find the range of y² y-2
Substituting y=2/x in y² y-2, we get:
y² y-2 = (2/x)² (2/x) - 2
= 4/x² (2/x) - 2
= 8/x³ - 2
Since x can be positive, negative or zero, we need to consider each case separately.
Case 1: x > 0
In this case, the range of y is (0, ∞)
Substituting x=1, we get:
y² y-2 = 8/1³ - 2 = 6
Substituting x→∞, we get:
y² y-2 → 0
Therefore, the range of y² y-2 for x > 0 is (0, 6]
Case 2: x < />
In this case, the range of y is (-∞, 0)
Substituting x=-1, we get:
y² y-2 = 8/(-1)³ - 2 = -6
Substituting x→-∞, we get:
y² y-2 → 0
Therefore, the range of y² y-2 for x < 0="" is="" [-6,="" />
Case 3: x = 0
In this case, y is undefined and y² y-2 is also undefined.
Step 3: Find b - 4a
Therefore, the range of y² y-2 is [-6, 6]
b - 4a = 6 - 4(-6) = 30
Therefore, the value of b - 4a is 30.
Solution:
Step 1: Find the range of y
y=2x/1 x² = 2/x
Since x is real, we know that x can be positive, negative or zero. However, we cannot have y=0 as it would make the denominator of the expression undefined.
Therefore, the range of y is (-∞, 0) U (0, ∞)
Step 2: Find the range of y² y-2
Substituting y=2/x in y² y-2, we get:
y² y-2 = (2/x)² (2/x) - 2
= 4/x² (2/x) - 2
= 8/x³ - 2
Since x can be positive, negative or zero, we need to consider each case separately.
Case 1: x > 0
In this case, the range of y is (0, ∞)
Substituting x=1, we get:
y² y-2 = 8/1³ - 2 = 6
Substituting x→∞, we get:
y² y-2 → 0
Therefore, the range of y² y-2 for x > 0 is (0, 6]
Case 2: x < />
In this case, the range of y is (-∞, 0)
Substituting x=-1, we get:
y² y-2 = 8/(-1)³ - 2 = -6
Substituting x→-∞, we get:
y² y-2 → 0
Therefore, the range of y² y-2 for x < 0="" is="" [-6,="" />
Case 3: x = 0
In this case, y is undefined and y² y-2 is also undefined.
Step 3: Find b - 4a
Therefore, the range of y² y-2 is [-6, 6]
b - 4a = 6 - 4(-6) = 30
Therefore, the value of b - 4a is 30.
Attention Class 11 Students!
To make sure you are not studying endlessly, EduRev has designed Class 11 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 11.
|
Explore Courses for Class 11 exam
|
|
Similar Class 11 Doubts
Top Courses for Class 11View all
consider y=2x/1+x², where x is real , then the range of expression y²+y-2 is [a,b]. Find b - 4a. Please solve this quadratic problem
Question Description
consider y=2x/1+x², where x is real , then the range of expression y²+y-2 is [a,b]. Find b - 4a. Please solve this quadratic problem for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about consider y=2x/1+x², where x is real , then the range of expression y²+y-2 is [a,b]. Find b - 4a. Please solve this quadratic problem covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for consider y=2x/1+x², where x is real , then the range of expression y²+y-2 is [a,b]. Find b - 4a. Please solve this quadratic problem.
consider y=2x/1+x², where x is real , then the range of expression y²+y-2 is [a,b]. Find b - 4a. Please solve this quadratic problem for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about consider y=2x/1+x², where x is real , then the range of expression y²+y-2 is [a,b]. Find b - 4a. Please solve this quadratic problem covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for consider y=2x/1+x², where x is real , then the range of expression y²+y-2 is [a,b]. Find b - 4a. Please solve this quadratic problem.
Solutions for consider y=2x/1+x², where x is real , then the range of expression y²+y-2 is [a,b]. Find b - 4a. Please solve this quadratic problem in English & in Hindi are available as part of our courses for Class 11.
Download more important topics, notes, lectures and mock test series for Class 11 Exam by signing up for free.
Here you can find the meaning of consider y=2x/1+x², where x is real , then the range of expression y²+y-2 is [a,b]. Find b - 4a. Please solve this quadratic problem defined & explained in the simplest way possible. Besides giving the explanation of
consider y=2x/1+x², where x is real , then the range of expression y²+y-2 is [a,b]. Find b - 4a. Please solve this quadratic problem, a detailed solution for consider y=2x/1+x², where x is real , then the range of expression y²+y-2 is [a,b]. Find b - 4a. Please solve this quadratic problem has been provided alongside types of consider y=2x/1+x², where x is real , then the range of expression y²+y-2 is [a,b]. Find b - 4a. Please solve this quadratic problem theory, EduRev gives you an
ample number of questions to practice consider y=2x/1+x², where x is real , then the range of expression y²+y-2 is [a,b]. Find b - 4a. Please solve this quadratic problem tests, examples and also practice Class 11 tests.
|
|
Explore Courses for Class 11 exam
|
|
Suggested Free Tests
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