In how many points graph of `y=x^3-3x2+5x-3` interest the x-axis?

Explanation

To find the number of points where the graph of the function \( y = x^3 - 3x^2 + 5x - 3 \) intersects the x-axis, we need to determine the roots of the equation \( x^3 - 3x^2 + 5x - 3 = 0 \).

### Step 1: Find the roots of the cubic equation
We will start by checking for rational roots using the Rational Root Theorem. We can test small integer values to see if they yield a root.

Let's test \( x = 1 \):
\[
f(1) = 1^3 - 3(1^2) + 5(1) - 3 = 1 - 3 + 5 - 3 = 0
...