Find the roots of x(^3) – 2x(^2) – 5x + 6 = 0

A.
1, 2, 3 
B.
1, 2, 3, 
C.
1, 2, 3 
D.
1, 2, 3
Correct Answer: Option A
Explanation
Equation: x(^3) – 2x(^2) – 5x + 6 = 0.
First, bring out a(_n) which is the coefficient of x(^3) = 1.
Then, a(_0) which is the coefficient void of x = 6.
The factors of a(_n) = 1; The factors of a(_0) = 1, 2, 3 and 6.
The numbers to test for the roots are (pm (frac{a_0}{a_n})).
= (pm (1, 2, 3, 6)).
Test for +1: 1(^3) – 2(1(^2)) – 5(1) + 6 = 1 – 2 – 5 + 6 = 0.
Therefore x = 1 is a root of the equation.
Using long division method, (frac{x^3 – 2x^2 – 5x + 6}{x – 1}) = x(^2) – x – 6.
x(^2) – x – 6 = (x – 3)(x + 2).
x = 2, 3.
(therefore) The roots of the equation = 1, 2 and 3.