The graphs of $ y=p(x) $ are given in Fig. $ 2.10 $ below, for some polynomials $ p(x) $. Find the number of zeroes of $ p(\bar{x}) $, in each case.
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Solution:
$( i).\ \because$ The given graph does not touch the $x-axis$ at any point. Thus, number of zeroes is $0$.
$( ii).\ \because$ The graph touches the $x-axis$ at one point. Thus, number of zeroes is $1$.
$( iii).\ \because$ The graph touches the $x-axis$ at three points. Thus, the number of zeroes is $3$.
$( iv).\ \because$ The graph touches the $x-axis$ at two points. Thus, the number of zeroes is $2$.
$( v).\ \because$ The graph touches the $x-axis$ at $4$ points. Thus, the number of zeroes is $4$.
$( vi).\ \because$ The graph touches the $x-axis$ at $3$ points. Thus, the number of zeroes is $3$.
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