The graph of $y=p(x)$ are given in fig below,

Question.

The graph of $\mathrm{y}=\mathrm{p}(\mathrm{x})$ are given in fig below, for some polynomials $\mathrm{p}(\mathrm{x})$. Find the number of zeros of $\mathrm{p}(\mathrm{x})$, in each case.

The graph of y


Solution:

(i) Graph of $y=p(x)$ does not intersect the $x$-axis. Hence, polynomial $p(x)$ has no zero.

(ii) Graph of $y=p(x)$ intersects the $x$-axis at one and only one point. Hence, polynomial $\mathrm{p}(\mathrm{x})$ has one and only one real zero.

(iii) Graph of $y=p(x)$ intersects the $x$-axis at 3 points. Hence, polynomial $p(x)$ has 3 zeros.

(iv) Graph of $y=p(x)$ intersects the $x$-axis at 2 points. Hence, polynomial $p(x)$ has 2 zeros.

(v) Graph of $y=p(x)$ intersects the $x$-axis at 4 points. Hence, polynomial $p(x)$ has 4 zeros.

(vi) Graph of $y=p(x)$ intersects the $x$-axis at 1 points and touch $x$-axis at 2 points. Hence, $p(x)$ has 3 zeros.

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