GATE 2017 CS (CS2) – Question 34
The equation x²−13x+36=0 has coefficients written in base b, and its roots in the same base are x=5 and x=6. Find b.
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Correct answer: 8.0 to 8.0
Explanation
The single-digit roots are decimal 5 and 6, so their sum is 11 and product 30. The coefficient 13 in base b is b+3, giving b+3=11 and b=8. The constant 36 is 3b+6=30 at b=8, confirming consistency.