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Tricky maths question. Find base of equation given solutions.

  1. Jan 12, 2013 #1
    1. The problem statement, all variables and given/known data
    5x2-50x+125 (equation 1)
    Solutions are x=5 and x=8

    (x-5)(x-8)
    = x2-13x+40 (equation 2)

    What is the base of the number system??

    2. Relevant equations


    3. The attempt at a solution
    Compare coefficients
    1a=5b
    -13a=-50b
    40a=125b

    The base must be greater than 8 since 8 is the highest solution..

    Descriminant of (1) is zero. Only one solution
     
    Last edited: Jan 12, 2013
  2. jcsd
  3. Jan 12, 2013 #2

    haruspex

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    I don't understand what you're doing there. What are a and b?
    How about taking the base to be a and writing out exactly what the equations mean in those terms, e.g. '125' becomes a2+2a+5.
     
  4. Jan 12, 2013 #3

    Dick

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    Saying 1=5 in any bases is nonsensical. The form of your equation must be C*(x-5)*(x-8) in any base. Doesn't that tell you what C must be?
     
    Last edited: Jan 12, 2013
  5. Jan 12, 2013 #4

    Yess whoops c=5
     
  6. Jan 12, 2013 #5

    Dick

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    Ok, so work it out in base 10 then equate it to the unknown base in (equation 1).
     
  7. Jan 12, 2013 #6
    Still not sure how I'm meant to solve for the base?!
     
  8. Jan 12, 2013 #7

    Dick

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    What's 5*(x-8)*(x-5) in base 10? The value of this expression doesn't depend on the base.
     
  9. Jan 12, 2013 #8
    okay shall give it a go!
     
  10. Jan 12, 2013 #9

    Dick

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    Try and stay on the forums instead of using private messaging. If you tell me why it's base 13, I'll probably tell you it's correct.
     
    Last edited: Jan 12, 2013
  11. Jan 15, 2013 #10
    looking only at the middle term, -50x of equation with unknown base, equating -5a=-65, we obtain a=13
     
  12. Jan 15, 2013 #11

    Dick

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    That's correct. You can check it by showing you get the same result from the last term.
     
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