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

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.