how
(5)b∗(6)b=(36)b means 30=3b+6
@Ani_
We can think as follows :
If we convert 5 and 6 in base b to base 10 , they will be 5 and 6 only.
Now, 5+6=(11)10=(13)b
Converting (13)b to base 10,
11= b+3 => b=8
Similarly,
5*6=(30)10=(36)b
Converting (36)b to base 10,
30= 3b+6 => b=8
very good explanation @VS
Answer is 8
The 2 roots of the eqtn are 5 and 6
The eqtn x2-13x+36 will be similar to (x-5)(x-6)
So, x2-13x+36 is similar to x2-11x+30
This tells us that (13)b = 11
=> 1*b1 + 3*b0 = 11
=> b+3 = 11
=>b = 8
Verify this by putting b=8 in (36)b = 30
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