- Study Anytime, Anywhere through Our Mobile App & Web Portal
- 1000+ Video Lectures by CAT/XAT Topper Faculties
- 400+ Hours content of CAT Preparation Videos
- 9000+ Questions in Online CAT Coaching Course
- 200+ Topic Based Tests (50+ Basic, 50+ Moderate & 50+ Advanced Level)
- 20+ CAT Mocks (Pro CATs – Best Online Tests Series for CAT)
- 10+ Mock OMETs (Online Test Series for SNAP, NMAT, IIFT, XAT, TISS, CMAT)
- Online Doubt Solving on One – to – One basis
- GD-PI-WAT Online Preparation Material
Get access to the detailed solutions to the previous years questions asked in IIM IPMAT exam
For real solution there are three cases possible:
Case I: (any integer)0 = 1
∴ x2 − 5x + 6 = 0
(x − 2)(x − 3) = 0
x = 2 or 3
Case II: (1)any integer = 1
∴ x2 − 15x + 55 = 1
x2 − 15x + 54 = 0
(x − 9)(x − 6) = 0
x = 6 or 9
Case III: (− 1)any even integer = 1
∴ x2 − 15x + 55 = − 1
x2 − 15x + 56 = 0
(x − 7)(x − 8) = 0
x =7 or 8
But we need to check whether the exponent x2 − 5x + 6 is even or not for x = 7 & 8.
Putting x = 7 in x2 − 5x + 6 we get 20,which is even.
Putting x = 8 in x2 − 5x + 6 we get 30, which is again even.
Thus both 7 and 8 are valid solutions,as well.
∴ Total the total number of real solutions for the given equation is 6 i.e (2, 3, 6, 9, 7, 8)