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Quadratic Equation question

  1. May 15, 2012 #1
    1. The problem statement, all variables and given/known data
    Find all the values of 'a', so that exactly one root of the equation x2-2ax+a2-1=0, lies between the numbers 2 and 4, and no root is either equal to 2 or equal to 4.


    2. Relevant equations



    3. The attempt at a solution
    Let f(x)=x2-2ax+a2-1
    I tried to visualize the question by graph. The graph could have been like this (this is only a rough sketch):-
    2qci6hi.jpg
    From here, i get three inequalities,
    f(2)<0 and f(4)>0 and D>0
    Solving these inequalities, i get a can lie in interval (1,3).
    But this is not the answer, the answer is (1,5)-{3}.
    Then i thought that graph could be also like this:-
    kb20d4.jpg
    But this gives completely different set of inequalities, now i am completely stuck.

    Any help is appreciated. :)
     
  2. jcsd
  3. May 15, 2012 #2
    The quadratic formula simplifies the root to a function of "a", no need to use graphs, I think your right btw (1,5)-{3} is the union of (1,3) and (3,5)
     
  4. May 15, 2012 #3

    I like Serena

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    Homework Helper

    Hey Pranav-Arora! :smile:

    Aha! You're drawing again. Good! :approve:

    Yep.

    Not stuck.
    This is indeed another set of inequalities that you also have to solve.
    The solution is the combination of both solutions.
     
  5. May 15, 2012 #4
    Oh yes, i knew about it, it will reduce to (x-a)2-1=0 and then we can proceed on the next steps. Thanks for the reply! :)

    Hello ILS! :smile:

    Thanks. :blushing:

    Now i understand it. Thanks once again! :smile:
     
  6. May 15, 2012 #5
    find the square and solve :D
     
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