IKMC 2024 - Grades 11-12 - Set 2 - Self-study Question 22

Question 22

Kangaroo solves $ax^2+bx+c=0$, and Beaver solves $bx^2+ax+c=0$, where $a,b,c$ are pairwise distinct nonzero integers. The equations share a solution. Which statement must be true?

The common solution must be 0
$ax^2+bx+c=0$ has exactly one real solution
$a>0$
$b<0$
$a+b+c=0$