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

Explanation

The number of points in which ` y = x^(3) - 3x^(2) + 5x - 3` intersects the x-axis is same as the number of real roots of the equation ` x ^(3) - 3x^(2) + 5x - 3 = 0`.
Now we can see that x = 1 satisfies the equation, hence one root of the equation is x = 1.
Now dividing ` x^(3) - 3x^(2) + 5x-3` by x - 1 , we have the quotient ` x^(2) - 2x + 3`.
Hence the equation reduces to `(x-1)(x^(2)-2x+3)= 0`.
Hence the only root of the equation is x = 1.
Thus, the graph of ` y = x^(3) - 3x^(2) + 5x - 3` cuts the x - axis in one point only.