MATHEMATICS

JAMB 2002 - Question 14

Mathematics 2002 JAMB Past Questions - Question 14: solve for x in the equation x³ - 5x² - x + 5 = 0

solve for x in the equation x³ - 5x² - x + 5 = 0
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 solve the equation x³ - 5x² - x + 5 = 0, we can use various methods such as factoring, the rational root theorem, or numerical methods. In this case, let's use the rational root theorem to find possible rational roots.The rational root theorem states that if a rational number p/q is a root of a polynomial equation, then p is a factor of the constant term (in this case, 5) and q is a factor of the leading coefficient (in this case, 1).The factors of 5 are ±1 and ±5, and the factors of 1 are ±1. Therefore, the possible rational roots are ±1, ±5.Let's try these values one by one:For x = 1:(1)³ - 5(1)² - 1 + 5 = 1 - 5 - 1 + 5 = 0So, x = 1 is a root.Now, we can use synthetic division to divide the polynomial by (x - 1):1 | 1 - 5 - 1 + 5  | 1 - 4 + 3  |_____________        -4 + 4 + 8The result is x² - 4x + 8.Now, we have a quadratic equation x² - 4x + 8 = 0. We can solve this using the quadratic formula:x = (-b ± √(b² - 4ac)) / (2a)For this equation, a = 1, b = -4, and c = 8.x = (-(-4) ± √((-4)² - 4(1)(8))) / (2(1))  = (4 ± √(16 - 32)) / 2  = (4 ± √(-16)) / 2Since the discriminant is negative, there are no real solutions for x. Therefore, the only real root of the original equation x³ - 5x² - x + 5 = 0 is x = 1.

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.