Question

Let ƒ(x) = ax³ + 5x² – bx + 1. If ƒ(x) when divided by

2x + 1 leaves 5 as remainder, and ƒ′(x) is divisible by 3x – 1 then –

• A. a = 26, b = 10
• B. a = 24, b = 12
• C. a = 26, b = 12
• D. None of these

Answer 1

Answer: (C)

a = 26, b = 12

Answer 2

ƒ(x) = ax³ + 5x² – bx + 1, ƒ′(x) = 3ax² + 10x – b

ƒ(–1/2) = 5, ƒ′(1/3) = 0

⇒ – $\frac{a}{8} + \frac{5}{4} + \frac{b}{2} + 1$ = 5, $\frac{3a}{9} + \frac{10}{3} - b = 0$

⇒ a = 26, b = 12.