Explanation
The correct answer 16, 8.
(235)R1 = (565)10 = (1065)R2 …….(1)
(235) R1 = 2R1^2 + 3R1 + 5 = 565 …………(2)
By solving quadratic equation (2) we get..
R1= 16 & -17.5
Since radix cannot be negative so ignore 17.5
Hence R1=16
Putting value of R1 in (1) we get -:
(235)16 =(1065)R2
2*16^2+3*16^1+5*16^0=1* R2^3 + 0* R2^2 + 6* R2^1 + 5* R2^0
512+48+5= R2^3+6R2+ 5
560= R2^3+6R2
R2^3+6R2-560=0
By solving above cubic equation we get-:
R2 = 8
R2 = -4 + i * 7.34847
R2 = -4 - i * 7.34847
Radix cannot be imaginary number so ignoring imaginary numbers
We get R2 = 8
From options we can see option B) is correct answer. Where R1 =16 and R2 =8.
