KEAM 2012 Math Paper

Given equations are
x2+ax+bc=0
and x2+bx+ca=0
On subtracting equation second from equation first
∴‌‌(a−b)x+c(b−a)=0
⇒‌‌(a−b)(x−c)=0
⇒x=c is the common root.
Thus, the roots of x2+ax+bc=0 are b and c
and that of x2+bx+ca=0 are c and a.
It roots are b and a, then equation will be
x2−(a+b)x+ab=0