GATE CS 2017 Set 2 — Question 24
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Digital Logic → Number Systems & Arithmetic → Number Base Conversions
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Question
Consider a quadratic equation with coefficients in a base . The solutions of this equation in the same base are and . Then b = ________.
Correct answer
8 to 8
Solution
Given the quadratic equation with roots and in base .In any base , for a quadratic equation , the sum of the roots is given by and the product of the roots is given by .
From the equation, sum
Equating the two:
From the equation, product
Equating the two: Both conditions yield . Additionally, for the base to be valid, all digits in the equation (1, 3, 6) and the roots (5, 6) must be strictly less than the base . Since , is a valid base.Therefore, the value of is 8.
1.Sum of roots:
Sum From the equation, sum
Equating the two:
2.Product of roots:
Product From the equation, product
Equating the two: Both conditions yield . Additionally, for the base to be valid, all digits in the equation (1, 3, 6) and the roots (5, 6) must be strictly less than the base . Since , is a valid base.Therefore, the value of is 8.
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