Final answer:
The zeros of the function are the x-values that make the function equal to zero. For the given function f(x) = x^4 - 4x^2 + 3x, the zeros can be found by factoring and solving for x, and each zero found will have a multiplicity of 1.
Step-by-step explanation:
The zeros of a function are the values of x for which the function equals zero. Given the function f(x) = x^4 – 4x^2 + 3x, we can find the zeros by setting the function equal to zero and solving for x.
To find the zeros, we factor where possible. The function can be factored as f(x) = x(x^3 – 4x + 3), which suggests one zero at x = 0 with multiplicity 1. We then look at the cubic x^3 – 4x + 3 and try to find its zeros by synthetic division, factoring, or using the Rational Root Theorem.
For the sake of the example and without further calculations provided, if we assume the cubic can be factored as (x-1)(x^2+x-3), we would get zeros at x = 1, x = −1 + √4, and x = −1 − √4. Each zero has multiplicity 1, since there are no repeated factors.