# 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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