<s>[INST] Find the base numeric system Find the numeric base we are using if $ x = 4 $ and $ x = 7 $ are zeros of $ 5x^2 - 50x + 118. $
When I plug in $ x = 4 $ and $ x = 7, $ I receive $ -2 $ and $ 13, $ respectively, but how do I proceed from that?
 [/INST] $$5_bx^2-50_bx+118_b=5_b(x-4_b)(x-7_b)$$
From $118_b$, we can assume that $b > 8$.
This implies $5_b = 5,\; 4_b = 4,\; 7_b = 7,\;$ and $\; 118_b = b^2 + b + 8$.
Hence
\begin{align}
   b^2 + b + 8 &= 5 \times 4 \times 7 \\
   b^2 + b - 132 &= 0 \\
   (b - 11)(b + 12) &= 0 \\
   b &= 11
\end{align}
CHECK:
\begin{align}
   5_{11}(x-4_{11})(x-7_{11})
   &= 5_{11}(x^2 - 10_{11}x + 26_{11}) \\
   &= 5_{11}x^2 - 50_{11}x +118_{11} \checkmark
\end{align}
</s>