SOLUTION: 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

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: 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      Log On


   

Question 134694: 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
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
If the roots are 5 and 8, then the equation can be written as
%28x-5%29%28x-8%29+=+0
(((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.