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Intro to Computer Engineering

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When solving 5x^2-50x+125=0, a space alien got x=8 for one of the two roots. What possible base could the alien be using? (Note: the coefficients are also in this base. That is 5,50,125 are all in this mystery base as well)

  • Intro to Computer Engineering - ,

    5*8^2 - 5b(8) + b^2+2b+5 = 0
    b^2 -38b + 325 = 0
    b = 13,25

    check:
    base 13
    5*8*8 = 328
    50*8 = 520
    125 = 200
    328-520+200 = 0

    base 25
    5*8*8 = 0 12 20 (base 25)
    125 = 1 2 5
    add: 1 15 0
    50*8 = 1 15 0
    subtract: 0

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