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finding base of quadratic system

bhuvanesh

Aug 29, 2013
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Aug 29, 2013
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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
 

Laplace

Apr 4, 2010
1,252
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1,252
The highest digit used in the problem statement is '8' therefore the base must be larger than eight.

In any number system with a base larger than eight the digits '5' and '8' always represent the same respective quantities.

In base ten the product 5x8=40 so a base larger than ten is needed for the product 5x8=37.
 
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