The graphs of $y = p(x)$ are given in figure below, for some polynomials $p(x)$. Find the number of zeroes of $p(x)$, in each case.
(i)
(ii)
(iii)
(iv)
(v)
(vi)
"
To do:
We have to find the number of zeroes of $p(x)$ in each case.
Solution:
(i) The given graph does not touch the x-axis at any point. Thus, the number of zeroes is $0$.
(ii) The graph touches the x-axis at one point. Thus, the number of zeroes is $1$.
(iii) The graph touches the x-axis at three points. Thus, the number of zeroes is $3$.
(iv) The graph touches the x-axis at two points. Thus, the number of zeroes is $2$.
(v) The graph touches the x-axis at $4$ points. Thus, the number of zeroes is $4$.
(vi) The graph touches the x-axis at $3$ points. Thus, the number of zeroes is $3$.
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