If the quadratic equations, x2+bx+c=0 and bx2+cx+1=0 have a common root then
b + c + 1 = 0
b2+c2−1=bc−b−c
b + c - 1 = 0
b2+c2+1=bc+b+c
Equations x2+bx+c=0 and bx2+cx+1=0 have a common root.
(bc−1)2=c−b2b−c2⇒b2c2+1−2bc=bc−b3−c3+b2c2⇒1+c3+b3=3bc⇒(1+c+b)c2+b2+1−b−c−bc=0⇒b+c+1=0 and c2+b2+1=c+b+bc