Math Is Fun Forum

  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2014-11-07 23:29:55

thedarktiger
Member
Registered: 2014-01-10
Posts: 91

Algebraic problemo

Let a,b be real numbers such that 0<b <= a.

Prove that the equation x^2+ax-b=0 cannot have two integer roots.


Good. You can read.

Offline

#2 2014-11-08 00:37:02

Olinguito
Member
Registered: 2014-08-12
Posts: 649

Re: Algebraic problemo

Suppose both roots are integers. Then a and b must both be integers and the discriminant is a perfect square. We have

[list=*]
[*]

[/*]
[/list]

Thus, if we want
to be a perfect square, we must have

[list=*]
[*]

[/*]
[/list]

Last edited by Olinguito (2014-11-08 01:18:13)


Bassaricyon neblina

Offline

Board footer

Powered by FluxBB