Question

Based on the graph of the polynomial function f(x)=3x⁴-41x³+19x²+89x+26, what is the degree of the polynomial and the number of real roots?

Answer 1

The degree of the polynomial function is 4. There are 2 or 0 real roots.

Step-by-step explanation:

The degree of a polynomial function is determined by the highest power of x in the function.

In this case, the highest power of x is 4, so the degree of the polynomial function f(x)=3x⁴-41x³+19x²+89x+26 is 4.

To determine the number of real roots, we need to consider the leading coefficient (3 in this case) and count the number of sign changes in the coefficients.

Since there are two sign changes in this polynomial, there are 2 or 0 real roots.