Respuesta :

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


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

The zeros of a function are the points where the graph crosses the x-axis.

The zeros of the function are: 0, 1 and 3, and the corresponding multiplicities are: 2, 1 and 1

The function is given as:

[tex]\mathbf{f(x) = x^4 - 4x^3 + 3x^2}[/tex]

Factor out x^2

[tex]\mathbf{f(x) = x^2(x^2 - 4x + 3)}[/tex]

Expand

[tex]\mathbf{f(x) = x^2(x^2 - 3x - x + 3)}[/tex]

Factorize

[tex]\mathbf{f(x) = x^2(x(x - 3) -1( x - 3))}[/tex]

Factor out x - 3

[tex]\mathbf{f(x) = x^2(x - 1)( x - 3)}[/tex]

Set to 0

[tex]\mathbf{x^2(x - 1)( x - 3) = 0}[/tex]

Split

[tex]\mathbf{x^2 = 0}[/tex]

[tex]\mathbf{x - 1 = 0}[/tex]

[tex]\mathbf{x - 3 = 0}[/tex]

Solve for x

[tex]\mathbf{x = 0}[/tex] --- with a multiplicity of 2 (i.e. the power of the expression)

[tex]\mathbf{x = 1}[/tex] --- with a multiplicity of 1

[tex]\mathbf{x =3}[/tex] --- with a multiplicity of 1

Hence, the zeros of the function are: 0, 1 and 3, and the corresponding multiplicities are: 2, 1 and 1

Read more about zeros and multiplicities at:

https://brainly.com/question/5992872

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