How do you use the rational roots theorem to find all possible zeros of $x^3 + 3x^2 - x - 3$ ?

Question

1174 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-27T04:44:56

Zeros are $-1. 1$ and $-3$

To find all possible zeros of $x^3+3x^2−x−3$ , we find rational roots of equation $x^3+3x^2−x−3=0$ . Factorizing

$x^3+3x^2−x−3=0$

= $x^2(x+3)-1(x+3)$

= $(x^2-1)(x+3)$

= $(x+1)(x-1)(x+3)$

Hence zeros are given by $x+1=0$ , $x-1=0$ and $x+3=0$ i.e.

Zeros are $-1. 1$ and $-3$

How do you use the rational roots theorem to find all possible zeros of x^3 + 3x^2 - x - 3x^3 + 3x^2 - x - 3?