For the equation ( 1 x+a - 1 x+b = 1 x+c ), if the product of roots is zero, then the sum of roots is

Step-by-step solution

( 1 x+a - 1 x+b = 1 x+c ) or (x^2+(a+b) x+a b=(b-a) x+(b-a) c ) or ( x ^2+2 ax + ab + ca - bc =0 ) Since product of the roots (=0 ) (a b+c a-b c=0 ; a= b c b+c ) Thus sum of roots (=-2 a= -2 b c b+c )