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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

User Rob Farley
by
7.1k points

2 Answers

6 votes

Answer:

So, the solutions are

There are only 2 real roots.

Explanation:

User Santosh Khalse
by
6.7k points
6 votes

Answer:

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.

User Tyler Clendenin
by
7.4k points