In how many points graph of $y = x^{3} - 3 x^{2} + 5 x - 3$ intersect the x-axis?

1

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2

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3

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0

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Solution

The correct option is A $1$
For intersection at x-axis
$0 = x^{3} - 3 x^{2} + 5 x - 3 \Rightarrow x^{3} - x^{2} - 2 x^{2} + 2 x + 3 x - 3 = 0 \Rightarrow (x^{2} - 2 x + 3) (x - 1) = 0$

Hence, $x = 1$ is the only point of intersection as
$(x^{2} - 2 x + 3) = 0$ has Discriminant $= - 8$ So , it will not intersect x-axis for any real value of x

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In how many points graph of y=x3−3x2+5x−3 intersect the x-axis?

The correct option is A 1For intersection at x-axis 0=x3−3x2+5x−3⇒x3−x2−2x2+2x+3x−3=0⇒(x2−2x+3)(x−1)=0Hence, x=1 is the only point of intersection as (x2−2x+3)=0 has Discriminant =−8 So , it will not intersect x-axis for any real value of x

In how many points graph of $y = x^{3} - 3 x^{2} + 5 x - 3$ intersect the x-axis?