Final answer:
To determine the total number of roots of a polynomial function, the complete polynomial is required to factor, find solutions using the Rational Zero Theorem or the Descartes' Rule of Signs.
Step-by-step explanation:
A polynomial function can have multiple roots, which are the values of x for which the function equals zero. To determine the total number of roots of the given polynomial function f(x) = 3x⁶+2x⁵+x⁴ - 2x³+6, we need to count the number of distinct real solutions. These solutions can be found by factoring the polynomial or using techniques like the Rational Zero Theorem or the Descartes' Rule of Signs.
However, without the complete polynomial, it is not possible to determine the total number of roots for the given polynomial.