If $x^2+bx+a=0$ and $x^2+ax+b=0$ have a common root $c$, Then what values of $(a,b)$ would work? Let $a$ and $b$ be distinct integers. If $x^2+bx+a=0$ and $x^2+ax+b=0$ have a common root $c$, Then which of the following statements are true?
1) $c*(a+c)=-b$
2) $a+b=-1$  
3) $a+b+c=0$ 
4) $c=0$ 
Update
I just tried to sub $c$ into both of the equations:
$c^2+cb+a=0$ and $c^2+ac+b=0$ which then gives us the equality
$c^2+cb+a=c^2+ac+b$
$ => cb+a=ac+b$
$=> b(c-1)=a(c-1)$
which gives me then a=b which is contradictory because the integers are supposed to be distinct.
Update #2
Ok it looks like 1) is true, 2) is true, 3) is true, and 4) is false .. right?

We know that $c^2+bc+a = 0$ and $c^2+ac+b = 0$. Subtract to get $c(b-a)-(b-a) = 0$ or $(b-a)(c-1) = 0$. This means that either $b = a$ or $c = 1$. If $c = 1$, then $1+a+b = c+a+b = 0$. 
