Number System The solution to the quadratic equation k 2 − 11k + 22 = 0 are x = 3 and x = 6. What is the base of the number system. (AKTU 2020) Let, the base = B Now, the equation is x 2 − 11x + 22 = 0 Now, x = 3 32 − 3(1xB 1 + 1xB 0 ) + (2xB 1 + 2xB 0 ) = 0 9 − 3(B + 1) + (2B + 2) = 0 B = 8 So, the base is 8. Hence, we are dealing with Octal. We will get the same result when we will deal with x = 6. Find value of x for the following equation: (135) x +(144) x =(323) x (RTU 2019) If the two numbers are equivalent, they will remain equal in other number systems as well. Converting both the sides to decimal and equating, we get: (1x 2 + 3x 1 + 5x 0 ) + (1x 2 + 4x 1 + 4x 0 ) = 3x 2 + 2x 1 + 3x 0 Hence, x 2 + 3x + 5 + x 2 + 4x + 4 = 3x 2 + 2x + 3 Solving x = 6 (Valid) These answers are taken from study material for B. Tech. exams for working professionals by amiestudycircle.com . With our study material which is prepared by IIT, Roorkee faculty (Retd.), no text book s...
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