Question

If (x – 1) is a factor of Ax³ + Bx² – 36x + 22 and 2^B = 64^A, find A and B ?

(a) A = 4, B = 16 

(b) A = 6, B = 24 

(c) A = 2, B = 12 

(d) A = 8, B = 16

Answer 1

(c) A = 2, B = 12 

Since (x – 1) is a factor of Ax³ + Bx² – 36x + 22

∴ A(1)³ + B(1)² – 36(1) + 22 = 0 

⇒ A + B = 14                    ...(i) 

and 2^B = 64^A ⇒ 2B = (26)^A ⇒ B = 6A           ...(ii)

∴ From (i) and (ii) A = 2, B = 12.