Question

The graphs of $y = p(x)$ are given in Fig. 2.10 below, for some polynomials $p(x)$ . Find the number of zeroes of $p(x)$, in each case(I)(ii)(iii)(iv)(v)(vi)

Answer 1

(i) The number of zeroes is $0$ as the graph does not cut the x-axis at any point.

(ii) The number of zeroes is $1$ as the graph intersects the x-axis at only $1$ point.

(iii) The number of zeroes is $3$ as the graph intersects the x-axis at $3$ points.

(iv) The number of zeroes is $2$ as the graph intersects the x-axis at $2$ points.

(v) The number of zeroes is $4$as the graph intersects the x-axis at $4$ points.

(vi) The number of zeroes is $3$ as the graph intersects the x-axis at $3$ points