GATE 2024 EC – Question 29
In a number system of base $r$, the equation $x^2-12x+37=0$ has $x=8$ as one of its solutions. The value of $r$ is ________.
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Correct answer: 11
Explanation
In base $r$, "12" means $r+2$ and "37" means $3r+7$. Substituting $x=8$: $64-8(r+2)+(3r+7)=0$, so $55-5r=0$ and $r=11$.