Question

The sum of real values of k for which the equation x3 - kx + k - 1 = 0 has exactly two distinct real solution is :
(A) 13/4 (B) 15/4 (C) 3/4 (D) 11/4

Answer 1

k = 3/4 + 3 = 15/4

OptionB is correct
Now, to get exactly two distinct real solutions , there are two cases possible .
Case 1 :
When (x*x+x +k -1) has both real equal roots and roots not equal to 1 .
Use Discriminant = 0 to get k= 3/4.

Case 2:
When one root of (x*x+x +k -1) is 1
implies k =3

Sum of all values =3+3/4= 15/4

Hope it becomes clear to you , if not call me again