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In how many points graph of y=x^3-3x2+5x...

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

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The umber of points in which `y =x^(3) - 3x^(3) + 5x - 3` inersect the x-axis is same as number of real roots of the equation `3^(3)-3x^(2) + 5x 0.`
Now we can see that x = 1 satisfies the equation, hence, one root of the equation is x = 1.
Now dividing `y =x^(3) - 3x^(3) + 5x - 3` by x-1, we have equotient `x^(2)-2x+3.` Hence, the equation reduces to `(x-1)(x^(2)-2x + 3) = 0` .
Now` x^(2)-2x+ 3 = 0 or (x - 1)^(2) + 2 = 0` is not ture for any real value of x .
Hence, the only root of the equation is x = 1.
Therefore, the graph of `y = x^(3)-3x^(2) + 5x-3` cuts the x-axis in one point only.
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