Find the value of k if the expression kx3 + x2 - 5x - 2...

Mathematics

JAMB 2006

Find the value of k if the expression kx³ + x² - 5x - 2 leaves a remainder 2 when it is divided by 2x + 1

A. 10
B. 8
C. -10
D. -8

WAEC and NECO CBT App for Mobile Devices - Candidates, Schools, Centres, Resellers - 100% Offline -Download Now

WAEC and NECO CBT Software for Computers and Laptops - Candidates, Schools, Centres, Resellers - 100% Offline -Download Now

Correct Answer: Option C

Explanation

F(x) = Q x D + R
Kx³ + x² - 5x – 2 = Q(2x+1)+R
If 2x+1 = 0 implies x = -¹/₂
∴k(-¹/₂)³ + (-¹/₂)² -5(-¹/₂) -2
= Q(2(-¹/₂) + 1) +2
K(-¹/₈) + ¹/₄ + ⁵/₂ - 2 = Q(-1+1)+2
-^k/₈ + ¹/₄ + ⁵/₂ - 2 = 0+2
(-k+2+20-16) / 8 = 2
(-k+6) / 8 = 2
-k+6 = 2*8
-k+6 = 16
-k = 16-6
-k = 10
∴k = -10

There is an explanation video available below.

Previous Next

Go back to Maths classroom

Report an Error Ask A Question Download App