Given, p(x) = x2 – 4
To find the zeros of p(x), consider p(x) = 0
∴ x2 – 4 = 0
(x – 2)(x + 2) = 0
Using the identity: (a2 – b2) = (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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