Identify the zeros of the polynomial \( f(x) = x^3 - 4x^2 + 5x \).

To find the zeros of the polynomial ( f(x) = x^3 - 4x^2 + 5x ), we can first factor the polynomial. Observing the polynomial, we notice that there is a common factor of ( x ):

[

f(x) = x(x^2 - 4x + 5)

]

Now, we have one zero that can be immediately identified as ( x = 0 ) from the factor ( x ).

Next, we need to find the zeros of the quadratic ( x^2 - 4x + 5 ). To do this, we can apply the quadratic formula, which is given by:

[

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

]

In our case, ( a = 1 ), ( b = -4 ), and ( c = 5 ). Plugging in these values, we compute:

[

x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4 \cdot 1 \cdot 5}}{2 \cdot 1} = \frac{4 \pm \sqrt