Question

Which of the following lists all the roots of x5-3x² + 3x³ - x² = 0?

A 0,-1
B -1,0,1
C 0,1
D -1,1

Answer 1

C

Explanation:

Well, the easiest way is to just plug in the numbers until they work :)

But if not, first notice
`x^2` as a common factor.

`x^5-3x^2+3x^3-x^2=0`

`x^2(x^3-3+3x-1)`

`x^2(x^3+3x-4)\\\\x^2(x+1)(x^2-x+4)\\`

Notice the leap in steps. I would be surprised if any teacher gave this question as a means to test your ability to factor though, it isn't easy for sure. Adding on, you cannot go further in this as 0, 1, and some imaginary numbers will be solutions.