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If a ∈ R and the equation -3 ( x - [ x])2 + 2 ( x- [ x])+a 2 =0 (where [x] denotes the greatest integer ≤ x ) has no integral solution, then all possible values of a lie in the interval: [JEE M 2014]
- a)( -2,-1)
- b)( -∞, -2 ) ∪ ( 2,∞ )
- c)( -1, 0 ) ∪ ( 0,1)
- d)(1,2 )
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If a ∈R and the equation -3 ( x - [ x])2 + 2 ( x- [ x])+a 2 =0 (w...
Consider –3(x – [x])2 + 2 [x – [x]) + a2 = 0
⇒ 3{x}2 – 2{x} –a2 = 0 (∵ x – [x] = {x})
⇒ 3{x}2 – 2{x} –a2 = 0 (∵ x – [x] = {x})
⇒
Now, {x} ∈ (0,1) and 
(by graph)
(by graph)Since , x is not an integer
∴ a ∈ (-1,1)- {0} ⇒ a ∈ (-1, 0)∪(0,1)
∴ a ∈ (-1,1)- {0} ⇒ a ∈ (-1, 0)∪(0,1)
Most Upvoted Answer
If a ∈R and the equation -3 ( x - [ x])2 + 2 ( x- [ x])+a 2 =0 (w...
Person is feeling sad, there are several things they can do to try and improve their mood. Here are some suggestions:
1. Reach out to a friend or loved one. Talking to someone you trust about how you're feeling can provide comfort and support.
2. Engage in activities that bring you joy. Whether it's reading, listening to music, watching a movie, or practicing a hobby, doing something you enjoy can help distract from negative emotions.
3. Take care of your physical health. Engaging in regular exercise, eating nutritious meals, and getting enough sleep can all have a positive impact on your mood.
4. Practice self-care. Take some time to relax and do something that makes you feel good, whether it's taking a bath, practicing mindfulness or meditation, or indulging in a favorite treat.
5. Seek professional help if needed. If feelings of sadness persist or become overwhelming, it may be helpful to reach out to a mental health professional who can provide guidance and support.
Remember, everyone's experience with sadness is unique, so it's important to find what works best for you.
1. Reach out to a friend or loved one. Talking to someone you trust about how you're feeling can provide comfort and support.
2. Engage in activities that bring you joy. Whether it's reading, listening to music, watching a movie, or practicing a hobby, doing something you enjoy can help distract from negative emotions.
3. Take care of your physical health. Engaging in regular exercise, eating nutritious meals, and getting enough sleep can all have a positive impact on your mood.
4. Practice self-care. Take some time to relax and do something that makes you feel good, whether it's taking a bath, practicing mindfulness or meditation, or indulging in a favorite treat.
5. Seek professional help if needed. If feelings of sadness persist or become overwhelming, it may be helpful to reach out to a mental health professional who can provide guidance and support.
Remember, everyone's experience with sadness is unique, so it's important to find what works best for you.
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If a ∈R and the equation -3 ( x - [ x])2 + 2 ( x- [ x])+a 2 =0 (where [x] denotes the greatest integer ≤ x ) has no integral solution, then all possible values of a lie in the interval: [JEE M 2014]a)( -2,-1)b)( -∞, -2 ) ∪ ( 2,∞ )c)( -1, 0 )∪ ( 0,1)d)(1,2 )Correct answer is option 'C'. Can you explain this answer?
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If a ∈R and the equation -3 ( x - [ x])2 + 2 ( x- [ x])+a 2 =0 (where [x] denotes the greatest integer ≤ x ) has no integral solution, then all possible values of a lie in the interval: [JEE M 2014]a)( -2,-1)b)( -∞, -2 ) ∪ ( 2,∞ )c)( -1, 0 )∪ ( 0,1)d)(1,2 )Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If a ∈R and the equation -3 ( x - [ x])2 + 2 ( x- [ x])+a 2 =0 (where [x] denotes the greatest integer ≤ x ) has no integral solution, then all possible values of a lie in the interval: [JEE M 2014]a)( -2,-1)b)( -∞, -2 ) ∪ ( 2,∞ )c)( -1, 0 )∪ ( 0,1)d)(1,2 )Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a ∈R and the equation -3 ( x - [ x])2 + 2 ( x- [ x])+a 2 =0 (where [x] denotes the greatest integer ≤ x ) has no integral solution, then all possible values of a lie in the interval: [JEE M 2014]a)( -2,-1)b)( -∞, -2 ) ∪ ( 2,∞ )c)( -1, 0 )∪ ( 0,1)d)(1,2 )Correct answer is option 'C'. Can you explain this answer?.
If a ∈R and the equation -3 ( x - [ x])2 + 2 ( x- [ x])+a 2 =0 (where [x] denotes the greatest integer ≤ x ) has no integral solution, then all possible values of a lie in the interval: [JEE M 2014]a)( -2,-1)b)( -∞, -2 ) ∪ ( 2,∞ )c)( -1, 0 )∪ ( 0,1)d)(1,2 )Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If a ∈R and the equation -3 ( x - [ x])2 + 2 ( x- [ x])+a 2 =0 (where [x] denotes the greatest integer ≤ x ) has no integral solution, then all possible values of a lie in the interval: [JEE M 2014]a)( -2,-1)b)( -∞, -2 ) ∪ ( 2,∞ )c)( -1, 0 )∪ ( 0,1)d)(1,2 )Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a ∈R and the equation -3 ( x - [ x])2 + 2 ( x- [ x])+a 2 =0 (where [x] denotes the greatest integer ≤ x ) has no integral solution, then all possible values of a lie in the interval: [JEE M 2014]a)( -2,-1)b)( -∞, -2 ) ∪ ( 2,∞ )c)( -1, 0 )∪ ( 0,1)d)(1,2 )Correct answer is option 'C'. Can you explain this answer?.
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