Question

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function? f(x) = (x3-3x+1)2

Answer 1

The degree of this polynomial is 3 x 2 = 6
Therefore, 6 roots exist.

Answer 2

The fundamental theorem of the algebra, establishes that for any polynomial of degree n, the roots of the polynomial are also n roots.

Where n is an integer greater than zero.

We then have the following function:

$f (x) = (x ^ 3-3x + 1) ^ 2$

We observe that the term of greatest exponent for the polynomial is:

$x ^ 6$

Therefore, the polynomial has 6 roots.

Answer:

exist 6 roots for the polynomial function