Question

What are the zeros of the function? What are their multiplicities? f(x)= x^4 - 4x^3 + 3x^2
a) the numbers -1 and -3 are zeros of multiplicity 2; the number 0 is a zero of the multiplicity 1
b) the number 0 is a zero of multiplicity 2; the numbers 1 and 3 are zeros of multiplicity 1
c) the numbers 0 and 1 are zeros of multiplicity 2; the number 3 is a zero of multiplicity 1
d) the number 0 is a zero of multiplicity 2; the numbers -1 and -3 are zeros of multiplicity 1

Answer 1

b is the correct answer. you see there x^2(x^2-4x+3) = 0
then x^2=0 or x= 1 or x=3. therefor x=0 with the multiplicity of 2 and x=1 and x=3 are the zeroes with multiplicity 1.