Question

How to find the radix of numbers in a quadratic equation?

Answer 1

Step-by-step explanation:

Let b be the desired radix; I’ll subscript the numbers that are written in this base; unsubscripted numbers are in base ten. (Note that one-digit numbers are unambiguous, so I don’t bother to subscript then.)

If x=5 is a solution to x2−10bx+31b=0, then 52−10b⋅5+31b=0. Now 10b=b, and 31b=3b+1, so what is b? If you’re still stuck, the conclusion is spoiler-protected below.