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Maths Question

  1. Aug 28, 2005 #1
    Hi,
    I may not be thinking straight or something, and im having trouble with this question, please help!:

    Given that 'p' is real, find the set of values of 'p' for which the roots of:
    (2p+1)x^2 - 10x + p-2 = 0
    a) Are real
    b) Have a sum>5

    Im thinking along the lines of: alpha+beta = -b/a and alpha x beta = c/a however I end up with 10/(2p+1) and (p-2)/(2p+1) respectively, which I cant work out simultaneously (2 equations for 3 variables).. Maybe im making something really stupid but please help.

    Thanks a lot for all your help.
     
  2. jcsd
  3. Aug 28, 2005 #2

    Tide

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    HINT: (a) findthe roots using the quadratic formula.

    (b) use the discriminant for the first condition.

    (c) add the roots for the second condition.
     
  4. Aug 28, 2005 #3
    Ahh thanks a ton! Don't know why I ignored those possibilities...
    Whilst we are on the topic, hehe, how would you draw 4<(x-4)^2 + (y-3)^2 <25 on a number plane? I can draw it on a cartesian graph using (x-4)^2 + (y-3)^2 = 25 and (x-4)^2 + (y-3)^2 = 4 but am confused as to how to transform this onto a simple number plane.. any hints there?
     
  5. Aug 28, 2005 #4

    Tide

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    That looks like a circle centered on (4, 3) and its radius is between 2 and 5.
     
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