Answer :

Given, p(x) = x^{2} – 4

To find the zeros of p(x), consider p(x) = 0

∴ x^{2} – 4 = 0

(x – 2)(x + 2) = 0

Using the identity: (a^{2} – b^{2}) = (a – b) (a + b)

x = 2 or x = –2

⇒ The real zeros of p(x) are 2 and –2, i.e. p(x) has two zeros.

To draw the graph of this polynomial, consider the following values of x and corresponding values of p(x):

Plotting these points on a graph paper as shown in the figure:

It can be observed that the graph of p(x) intersects the X-axis at two distinct points (–2, 0) and (2, 0).

The X–coordinates of these point are considered as zeros of p(x).

Thus, –2 and 2 are the zeros of p(x).

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