Question

Find the number of roots for the following equation.

4x^6+11x^5-x^3+3x+4=0

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the number of roots for the equation, we can look at the degree of the equation. The degree of an equation is the highest power of x in the equation.

In this case, the degree of the equation is 6, which means there can be a maximum of 6 roots.

However, this does not necessarily mean that there are exactly 6 roots. The number of roots can be less than or equal to the degree of the equation.

To determine the exact number of roots, we need to use the concept of the Fundamental Theorem of Algebra.

The Fundamental Theorem of Algebra states that any polynomial equation of degree n has exactly n roots, including complex roots.

In the given equation, the degree is 6, so there can be a maximum of 6 roots, including complex roots.