Tricky maths question. Find base of equation given solutions.

[tigertan]

Homework Statement

5x²-50x+125 (equation 1)
Solutions are x=5 and x=8

(x-5)(x-8)
= x²-13x+40 (equation 2)

What is the base of the number system??

Homework Equations

The Attempt at a Solution

Compare coefficients
1_a=5_b
-13_a=-50_b
40_a=125_b

The base must be greater than 8 since 8 is the highest solution..

Descriminant of (1) is zero. Only one solution

 

[haruspex]

Compare coefficients
1_a=5_b

I don't understand what you're doing there. What are a and b?
How about taking the base to be a and writing out exactly what the equations mean in those terms, e.g. '125' becomes a²+2a+5.

 

[Dick]

Saying 1=5 in any bases is nonsensical. The form of your equation must be C*(x-5)*(x-8) in any base. Doesn't that tell you what C must be?

 

[tigertan]

Saying 1=5 in any bases is nonsensical. The form of your equation must be C*(x-5)*(x-8) in any base. Doesn't that tell you what C must be?

Yess whoops c=5

 

[Dick]

Yess whoops c=5

Ok, so work it out in base 10 then equate it to the unknown base in (equation 1).

 

[tigertan]

Still not sure how I'm meant to solve for the base?!

 

[Dick]

Still not sure how I'm meant to solve for the base?!

What's 5*(x-8)*(x-5) in base 10? The value of this expression doesn't depend on the base.

 

[tigertan]

okay shall give it a go!

 

[Dick]

okay shall give it a go!

Try and stay on the forums instead of using private messaging. If you tell me why it's base 13, I'll probably tell you it's correct.

 

[tigertan]

looking only at the middle term, -50x of equation with unknown base, equating -5a=-65, we obtain a=13

 

[Dick]

looking only at the middle term, -50x of equation with unknown base, equating -5a=-65, we obtain a=13

That's correct. You can check it by showing you get the same result from the last term.