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Math Help - Finding unknown base from equation

  1. #1
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    Finding unknown base from equation

    I am given this equation of an unknown base:
    x^2 - 10x +25
    It has a solution of x=5 and x=8 which are likely to be in our base 10.

    I tried to find out the unknown base by comparing the co-efficients of the equations by doing so:
    (x-5)(x-8) = x^2 - 13x + 40  <--in base 10
    x^2 - 10x +25  <--in unknown base

    Then I try to solve for the unknown base:
    1*b = 13, b=13
    but...
    5*1 + 2*b = 40
    2b = 35
    b=17.5

    How can the b in the equations be different? If this is the case, what is the actual base for the equation?
    thanks!
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  2. #2
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    Quote Originally Posted by xEnOn View Post
    I am given this equation of an unknown base:
    x^2 - 10x +25
    It has a solution of x=5 and x=8 which are likely to be in our base 10.

    I tried to find out the unknown base by comparing the co-efficients of the equations by doing so:
    (x-5)(x-8) = x^2 - 13x + 40  <--in base 10
    x^2 - 10x +25  <--in unknown base

    Then I try to solve for the unknown base:
    1*b = 13, b=13
    but...
    5*1 + 2*b = 40
    2b = 35
    b=17.5

    How can the b in the equations be different? If this is the case, what is the actual base for the equation?
    thanks!
    The equations you bet are inconsistent, which is what I find. So there is no solution to the problem as you post it.

    Check the exact wording of the question, and post that.

    Also this is not a number theory question, so I am moving the thread to the algebra section.

    CB
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  3. #3
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    Thanks for moving to the correct section.

    The equation from the question was: 5x^2 -50x +125 in an unknown base with x=5 and x=8.
    The question was to find the unknown base of the question. I divided by 5 on the coefficients before trying to find out the base.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by xEnOn View Post
    Thanks for moving to the correct section.

    The equation from the question was: 5x^2 -50x +125 in an unknown base with x=5 and x=8.
    The question was to find the unknown base of the question. I divided by 5 on the coefficients before trying to find out the base.
    Now use the same method as before, so in base 10:

    5(x-5)(x-8)=5x^2-(5b)x+(b^2+2b+5)

    and this time it works.

    CB
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  5. #5
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    thanks CaptainBlack.
    But what is the reason for adding a b this way? And why wouldn't my previous method work?

    I calculated the equation and for (5b)x, b=13 but the b^2 + 2b +5, b=13.892 or -13.892. So is 13 considered the base enough though there is 0.892 more?
    Last edited by xEnOn; January 29th 2011 at 11:33 PM.
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  6. #6
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    ok i figured out how the 'b's come into the equation. but still, I am getting b=13 from 5b and b=13.892 or b=-13.892 from b^2 + 2b +5. It is weird that the 2 don't give similar results. then how can I determine its base?
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  7. #7
    Grand Panjandrum
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    Quote Originally Posted by xEnOn View Post
    ok i figured out how the 'b's come into the equation. but still, I am getting b=13 from 5b and b=13.892 or b=-13.892 from b^2 + 2b +5. It is weird that the 2 don't give similar results. then how can I determine its base?
    Your arithmetic is wrong, b=13 is a root of 200=b^2+2b+5

    CB
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  8. #8
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    oh yea! you are right about that. I had some calculation mistakes earlier..
    thank you so much!
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