0

Guest

Courses New

Let ' ƒ' be continuous function defined on [-2009 , 2009 ] such that ƒ(x) is irrational for each x belongs to [-2009 , 2009] and ƒ(0)=2+√3+√5 . the equation ƒ(2009)x 2 + 2ƒ(0)x + ƒ(2009) = 0 has ? 1 ) only rational roots 2 ) only rational roots 3 ) one rational and one irrational root 4 ) imaginary roots which is the appropriate answer explain ?

Let  ' ƒ'  be continuous function defined on [-2009 , 2009 ]  such that ƒ(x) is irrational  for each   x belongs to [-2009  ,  2009]


and   ƒ(0)=2+√3+√5  .  the equation         ƒ(2009)x2  + 2ƒ(0)x + ƒ(2009) = 0 has  ?


 


 




  • 1 )  only rational roots 

  • 2 )  only rational roots

  • 3 )  one rational and one irrational root

  • 4 )  imaginary roots     


    •           which is the appropriate answer  explain ?

    Grade:

    1 Answers

    AJIT AskiitiansExpert-IITD
    68 Points
    13 years ago

    Dear Chitikala ,

    Well , the catch is that the function is irrational and continuous on the domain . so you think how can a function be both irrational and continuous. if f(x) will have any other value than f(0) , it will leave all the rational points in between so won't be continuous, which implies it won't take any other value than f(0). so f(x) is a constant function over [-2009 , 2009] having the value f(0).

     i.e f(-2009)=f(-2008)........f(0)= f(1)=f(2)=f(3)= ..............f(2009) , so

    equation becomes   x2  + 2x + 1 = 0   . so , roots are 1 and 1 . therefore option 1) is correct.

    Please feel free to post as many doubts on our discussion forum as you can. We are all IITians and here to help you in your IIT JEE preparation.

    Now you can win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.

    Win exciting gifts by answering the questions on Discussion Forum..

                                                                         
                                                                         
                                                                         
                                                 
     

     





    Think You Can Provide A Better Answer ?

    Other Related Questions on Algebra

    View all Questions »

    ASK QUESTION

    Get your questions answered by the expert for free

    Answer and earn gift vouchers

    Win Gift vouchers upto Rs 500/-

    View courses by askIITians

    Design classes One-on-One in your own way with Top IITians/Medical Professionals

    Click Here Know More

    Complete Self Study Package designed by Industry Leading Experts

    Click Here Know More

    Live 1-1 coding classes to unleash the Creator in your Child

    Click Here Know More

    a Complete All-in-One Study package Fully Loaded inside a Tablet!

    Click Here Know More