The roots of the equation `x^(3) -2x^(2) -x +2 =0` are

Options

A. 1,2,3
B. `-1,1,2`
C. `-1,0,1`
D. ` -1,-2,3`

Answer

To find the roots of the equation \( x^3 - 2x^2 - x + 2 = 0 \), we can use the Rational Root Theorem and synthetic division to identify possible rational roots. Let's solve the equation step by step.

### Step 1: Identify Possible Rational Roots
According to the Rational Root Theorem, the possible rational roots of the polynomial can be the factors of the constant term (which is 2) divided by the factors of the leading coefficient (which is 1). The factors of 2 are \( \pm 1, \pm 2 \).