[MOVED] finding base of quadratic system

[Bhuvanesh123]

The roots of the quadratic equation x^2-12x+37=0 are 5 and 8. Find the base system in which this equation is written

If the roots are 5 and 8, then the equation can be written as
(((x^2 -(5+8)x + (5*8) = 0}}}
so in what base is 5+8 = 12 and 5*8 = 37?
The base must be greater that 8 since one of the solutions is 8.
The base is greater than 10 since 5*8 base 10 is 40 and our product is 37
Try 11. Hey, it works!
5+8 base 11 = 12 and (5*8) base 11 = 37.

How they say the base should be greater than 8 and also than 10..thank you in advance

 

[ads-ee]

The base is greater than 8 because 8 is a digit in the base system used.

If 5*8 in base 10 is 40 but the answer is 37 the base has to be be greater than 10.
This is similar to saying 16 (base10) is 10 (base16)

 

[albbg]

What said by ads-ee is correct. However you can write:

5+8=b+2
5*8=3*b+7

both of them give b=11