Question

12. Consider the function ƒ(x) = x^4 – x^3 + 2x^2 – 2x. How many real roots does it have?

options:
A) 2
B) 1
C) 3
D) 4

Answer 1

So, the solutions are

There are only 2 real roots.

Explanation:

Answer 2

Explanation:

Hello, let's factorise as much as we can.

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

So, the solutions are

`0, \ 1, \ √(2)\cdot i, \ -√(2)\cdot i`

There are only 2 real roots.

Thank you.