Question

the graph of polynomial p (x) intersect the x axis 3 times on distinct points of the number of zeros​

Answer 1

The number of zeroes is 3.

The graph of the polynomial p(x) intersects the x-axis 3 times on distinct points. The number of zeroes of p(x) is 3.

Step-by-step explanation:

Given that, the polynomial p(x) intersects the x-axis three times on distinct points.

Let (a, 0), (b, 0) and (c, 0) be those intersections, where a ≠ b ≠ c.

Then we can form the polynomial p(x) as follows,

p(x) = (x - a) (x - b) (x - c)

It gives that p(x) has three zeores a, b and c.

If we try to draw a polynomial with three zeroes, we arrive at a graph that intersects the x-axis three times. (Refer to the attached image)

Here, p(x) = (x - 1) (x - 2) (x - 3)

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