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

Question

1042 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#