What are all the roots of x^3 - 3x^2 - x +3 = 0?

Question

callisto · Answer

1. do factorization
 x^2(x - 3) - (x -3) = 0
 (x^2-1)(x-3)          =0
 (x-1)(x+1)(x-3)      =0
2. for it to exist, either  (x-1)=0  or  (x+1)=0  or  (x-3)=0
Can you solve them for here?

callisto · Answer

*delete the word ''for''

anonymous · Answer

The answers are -1 and 1, 1 and 3, -1,1, and 3, 1, -1, and 3. So the answer would be the last one correct?

callisto · Answer

-1,1, and 3, 1, -1, and 3. <- any differences?

anonymous · Answer

Yes, because the way you set it up the last one would only work because in the first one -1 - 1 is -2 not zero, so I guess it might be a trick question? I have no idea

callisto · Answer

*confused*
I assume  your 3rd choice is -1, 1 and 3
the 4th choice is 1, -1 and 3
Numerically, aren't they supposed to be the same?

callisto · Answer

And you need to know that you have to solve the 3 equations independently.
(x-1)=0  or  (x+1)=0  or  (x-3)=0
x = 1      or   x =-1     or       x=3
So, you'll get 3 numbers.. and from your choices, I can hardly recognise their differences except the arrangement of the answers.

anonymous · Answer

Here is the question from the book.

callisto · Answer

lol you've made a typing mistake for the last choice :P

anonymous · Answer

Oh, lol sorry about that haha!

callisto · Answer

Can you get the answer now?

anonymous · Answer

Yes! Thanks for the help.

callisto · Answer

welcome :)