GATE ECE 2024 | Question: 19

Question

In a number system of base $r$, the equation $x^{2}-12 x+37=0$ has $x=8$ as one of its solutions. The value of $r$ is $\_\_\_\_\_\_\_$.

Answer 1

Note: The given Equation is in number system of base r

so given Equation :x^2-12x+37=0

convert 12 and 37 in base r number system

12=1.r^1+2.r^0=(r+2)

37=3.r^1+7.r^0=(3r+7)

-->x^2-(r+2)x+(3r+7)=0

-->64-8r-16+3r+7=0  (x=8 given)

-->55-5r=0 and r=11