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

F ( x ) = x² ( x² - 4 x + 3 ) =
= x² ( x² - 3 x - x + 3 ) =
= x² ( x ( x - 3 ) - ( x - 3 ) ) =
= x² ( x - 3 ) ( x - 1 ) = 0
x² = 0 ⇒ x = 0
x - 3 = 0 ⇒ x = 3
x - 1 = 0 ⇒ x = 1
The zeroes of the function are: x = 0, x = 1 and x = 3.

B ) The number 0 is a zero of multiplicity 2; the numbers 1 and 3 are zeroes of the multiplicity 1.