Question

Determine where the real zeros of f(x)=x^4-2x^3+x-2 are located.

a.
at -1 & 2
c.
at 0 & 1
b.
at 1 & 2
d.
at -1 & 1

Answer 1

a. at -1 & 2

Explanation:

The given function is

`f(x)=x^4-2x^3+x-2`.

Equate the function to zero.

`x^4-2x^3+x-2=0`.

Factor by grouping;

`x^3(x-2)+1(x-2)=0`

Factor further;

`(x-2)(x^3+1)=0`

Apply the zero product property;

`(x-2)=0,(x^3+1)=0`

Solve for x;

`x=2,x^3=-1`

`\Rightarrow x=2,x=\sqrt[3]{-1}`

`\therefore x=2,x=-1`