Question

Use the Rational Root Theorem to list all possible rational roots of the polynomial equation x3 – x2 – x – 3 = 0. Do not find the actual roots. (1 point)
–3, –1, 1, 3
1, 3
–33
no roots

Answer 1

Hello,
List all possible rational roots of the polynomial equation x3 – x2 – x – 3 = 0

Answer -1,1,-3,3
but none is a root.

Answer 2

The Cubic Polynomial  given here is

x³ - x² - x -3 =0

Rational root theorem :

Consider any polynomial

→ $Ax^n +A_{1}x^{n-1}+A_{2}x^{n-2}+.................+A_{n}=0$

So, the factors of this polynomial is those number which divides $\frac{A_{n}}{A}$.Which are $\pm1, \pm\frac{A_{n}}{A}$

Applying the same method the number which divides (-3) are,-3,+3,-1,+1. So By rational root theorem all the factors of this cubic polynomial is $\pm1,\pm3$.

Option 1. -3,-1,1,3 is correct option.