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 $\mathrm{y}=\mathrm{p}(\mathrm{x})$ 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.
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.
(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.