Final answer:
The student aims to find the zeros of the polynomial function f(x)=2x⁴-x³-6x²+7x-2 and their multiplicities, which involves identifying values of x that satisfy f(x) = 0, either algebraically or using a graphing calculator.
Step-by-step explanation:
The student is seeking to find the zeros of the polynomial function f(x)=2x⁴-x³-6x²+7x-2 and determine their multiplicities. In order to find the zeros of a polynomial, different methods can be employed, such as factoring, synthetic division, or using the quadratic formula if the polynomial can be reduced to a quadratic equation.
Identifying the zeros requires finding the values of x that satisfy the equation f(x) = 0. It's important to note that for higher degree polynomials, it's not always possible to find all roots algebraically, and numerical methods or graphing calculators might be used.
Once the zeros are found, multiplicity can be determined by the number of times each root makes the function equal to zero.