What are the zeros of the function? what are their multiplicities? f(x)=x^4-4x^3+3x^2

Since each term contains x, x= 0 is one answer Also as x^2 is a factor  it has duplicity 2.
Factoring:-

x^2 (x^2 - 4x + 3) = 0
x^2( x - 3)(x - 1) = 0

so x = 3 and x = 1 are also zeros

-   x = 0 (duplicity 2), x = 1 and x = 3.