MATHEMATICS

JAMB 2000 - Question 19

Mathematics 2000 JAMB Past Questions - Question 19: If (x-1), (x+1) and (x-2) are factors of the polynomial ax³ +bx+cx -1, find a,b,c receptively

If (x-1), (x+1) and (x-2) are factors of the polynomial ax³ +bx+cx -1, find a,b,c receptively
A:
B:
C:
D:
Examkits App

Examkit's JAMB CBT App

Practice JAMB offline with our Online, PC and Mobile App

  • ✅ 25+ years of past questions (2000 to 2025)
  • ✅ Video solutions and explanation to questions
  • ✅ E-library
  • ✅ Study by topic
  • ✅ And more.

Correct Answer

A

Explanation

To find the values of a, b, and c, we can use the fact that if (x - 1), (x + 1), and (x - 2) are factors of the polynomial, then when we substitute x = 1, x = -1, and x = 2 into the polynomial, the result should be zero.Let's substitute x = 1 into the polynomial:a(1)³ + b(1) + c(1) - 1 = 0a + b + c - 1 = 0 ----(1)Now, substitute x = -1 into the polynomial:a(-1)³ + b(-1) + c(-1) - 1 = 0-a - b - c - 1 = 0 ----(2)Finally, substitute x = 2 into the polynomial:a(2)³ + b(2) + c(2) - 1 = 08a + 2b + 2c - 1 = 0 ----(3)We now have a system of three equations (equations 1, 2, and 3) with three unknowns (a, b, and c). We can solve this system of equations to find the values of a, b, and c.Adding equations (1) and (2), we get:2b = 0b = 0Substituting b = 0 into equations (1) and (2), we have:a + c - 1 = 0 ----(4)-a - c - 1 = 0 ----(5)Adding equations (4) and (5), we get:0 = 0This means that the equations (4) and (5) are dependent, and we cannot determine the values of a and c independently. This implies that there are infinitely many possible values for a and c that satisfy the given conditions.In conclusion, we can determine that b = 0, but the values of a and c can vary.

Frequently Asked Questions

Examkits is a JAMB CBT practice platform that provides over 20 years of past questions, Post UTME questions, and detailed video solutions to help students prepare for their exams.

You can practice JAMB past questions online, on Android, or on a desktop using the Examkits app. Just register on our website and choose your preferred device.

Yes. Our Android and Windows versions support offline usage. Once downloaded and activated, no internet is required to use most of the features.

Yes, Examkits provides detailed video explanations for all JAMB past questions from 2000 to 2024, helping students understand how to solve each problem.

Examkits offers free practice for some subjects. However, full access requires a one-time affordable activation fee for each version of the app.