Chapter 8.9, Problem 1ST

To determine

To state: that $x^3+2x^2-x+3=0$ has no rational roots.

Answer to Problem 1ST

The polynomial does not have any rational root.

Explanation of Solution

Given information:

The polynomial is $x^3+2x^2-x+3=0$ .

the polynomial have possible rational roots are $\pm 1\text{ and }\pm 3$ ,

Since the possible rational roots do not satisfy the polynomial equation.

Thus, the polynomial equation does not have any rational root.