Question

what is the total number of roots for the following equation? y = 4x⁶ - 12x⁵ - x⁴ + 2x³ - 6x² - 5x + 10

Explanation:

Step1: Identify polynomial degree

The given polynomial is $y=4x^6-12x^5-x^4+2x^3-6x^2-5x+10$. The highest power of $x$ is 6, so the degree $n=6$.

Step2: Apply Fundamental Theorem of Algebra

A polynomial of degree $n$ has exactly $n$ roots (counting real and complex, with multiplicity). For $n=6$, the total number of roots is 6.

Answer:

6