If the quadratic equation x^2+(2- ) x-(1+ )=0 has two integral roots, then sum of all possible values of in the interval (0,2 ) is k , then the value of k is equal to

Step-by-step solution

aligned & x ^2+(2- ) x -(1+ )=0 & + = -2....(i) & =- -1 aligned From equation (1) +(2) aligned & + + =-3 & ( +1)( +1)=-2 aligned Hence either +1=-2 and +1=1 then =-3, =0 or +1=-1 and +1=2 =-2 and =1 If =-3, =0 then =-1 = 3 4 , 7 4 If =-2, =1 then =1 = 4 , 5 4 Sum = 3 4 + 7 4 + 4 + 5 4 =4 =4