Question

Given that b³+mb² +nb + c is divisible by (b-s) if s³ + ms² + ns + c = 0Also given that d³+d²+ed+1 is divisible by (d-1) and d³-4d²+fd-3 is divisible by (d-3)What is the value of e+f ?

• A. -1
• B. 1
• C. 2
• D. none of these

Answer 1

The correct option is B 1

Option (c)

d³+d²+ed+1 is divisible by (d-1). As 1 is a root, Put d=1 in the equation and equate it to 0, to get the value of e

1+1+e+1=0 e=-3

Similarly put d=3 in d³-4d²+fd-3 to get the value of f

27-36+3f-3=0 3f=12 f=4

e+f= -3+4=1