Please wait...
Contact Us
Contact
Need assistance? Contact us on below numbers

For Study plan details

93219 24448 / 89292 63204

10:00 AM to 7:00 PM IST all days.

For Franchisee Enquiry

81783 72169
OR

Chat with us on WhatsApp

or

Thanks, You will receive a call shortly.
Customer Support

You are very important to us

For any content/service related issues please contact on this number

93219 24448 / 99871 78554

Mon to Sat - 10 AM to 7 PM

Home / Doubts and Solutions/JEE/Test Resources

give answer of both paragraphs

Asked by rbhatt16 12th October 2017, 5:10 PM
Answered by Expert
Answer:
Let us find the condition for one root < 2 and other root >2
 
begin mathsize 12px style x squared minus left parenthesis m minus 3 right parenthesis x space plus space m space equals space 0 r o o t s space a r e space fraction numerator left parenthesis m minus 3 right parenthesis plus-or-minus square root of open parentheses m minus 3 close parentheses squared minus 4 m end root over denominator 2 end fraction space semicolon space t h i s space c a n space b e space w r i t t e n space a s space space fraction numerator left parenthesis m minus 3 right parenthesis plus-or-minus square root of open parentheses m minus 1 close parentheses left parenthesis m minus 9 right parenthesis end root over denominator 2 end fraction L e t space t h e space s m a l l e r space r o o t space space fraction numerator left parenthesis m minus 3 right parenthesis minus square root of open parentheses m minus 1 close parentheses left parenthesis m minus 9 right parenthesis end root over denominator 2 end fraction space less than 2 left parenthesis m minus 3 right parenthesis minus square root of open parentheses m minus 1 close parentheses left parenthesis m minus 9 right parenthesis end root space less than space 4 space space left parenthesis m minus 7 right parenthesis space less than space square root of open parentheses m minus 1 close parentheses left parenthesis m minus 9 right parenthesis end root m squared minus 14 m plus 49 space less than space m squared minus 10 m plus 9 t h i s space g i v e s space t h e space c o n d i t i o n space space m space greater than space 10 end style
begin mathsize 12px style L e t space t h e space b i g g e r space r o o t space fraction numerator left parenthesis m minus 3 right parenthesis plus square root of open parentheses m minus 3 close parentheses squared minus 4 m end root over denominator 2 end fraction space space greater than space 2 h e n c e space space square root of open parentheses m minus 1 close parentheses open parentheses m minus 9 close parentheses end root space greater than space left parenthesis 7 minus m right parenthesis space left parenthesis p l e a s e space w o r k o u t space t h e space a l g e b r a space a s space d o n e space i n space p r e v i o u s space c a s e right parenthesis h e n c e space m squared minus 10 m plus 9 space greater than space m squared minus 14 m plus 49 space a n d space t h i s space l e a d s space t o space m space greater than 10 end style
So the answer is m lies between 10 and ∞   (10, ∞ )
 
-------------------------------------------
 
for both roots >2
 
if we work out same way as above for smaller root we get m<10 and for bigger root m>10
 
but we need begin mathsize 12px style square root of left parenthesis m minus 3 right parenthesis squared minus 4 m end root end style should be positive and this leads the condition m > 9.
Hence the answer is m lies between 9 and 10 , (9,10)
 
------------------------------------------
 
if you work out same way, for one root > 1 and other root <2 again the answer is (9,10)
 
 
The question related to second paragraph is not answered because for one post only one question is allowed

Answered by Expert 18th October 2017, 12:32 PM
Rate this answer
  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
  • 7
  • 8
  • 9
  • 10

You have rated this answer /10

Report an issue
Previous Question
Next Question
Your answer has been posted successfully!

Free related questions

RELATED STUDY RESOURCES :
JEE QUESTION ANSWERS

Chat with us on WhatsApp