Question

The graphs of $y=p\left(x\right)$ are given in the figure, for some polynomials $p\left(x\right)$. Find the number of zeroes of $p\left(x\right)$, in each case.

Answer 1

(i) The graph does not intersect the $x$-axis, so there are no zeros in $p\left(x\right)$.

(ii) The graph intersects the $x$-axis at one place, so here there is one zero in $p\left(x\right)$.

(iii) The graph intersects the $x$-axis at three places, so that there are three zeros in $p\left(x\right)$.

(iv) The graph intersects the $x$-axis at two places, so here there are two zeros in $p\left(x\right)$.

(v) The graph intersects the $x$-axis at four places, so there are four zeros in $p\left(x\right)$.

(vi) The graph intersects the $x$-axis at three places, so that there are three zeros in $p\left(x\right)$.