The cubic polynomial $f (x) = x^{3} - 5 x^{2} + 8 x - 4$ has distinct zeros.

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Solution

Draw the graph of $f (x) = x^{3} - 5 x^{2} + 8 x - 4$

We see that the graph intersects the x-axis at $2$ distinct points, hence we say that
$f (x) = x^{3} - 5 x^{2} + 8 x - 4$ has $2$ distinct zeros.

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