Question

What are the zeroes of the function? What are their multiplicities?

f (x) = x^4 – 4x^3 + 3x^2



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

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

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

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

Answer 1

factor
\[x^2(x^2-4x+3)\]
to
\[x^2(x-1)(x-3)\]
The zeros are 0(twice), 1, 3
multiplicity states how often the zero is