Polynomials ⇒⇒ 2.1

Question 1 (i)

The graphs of y = p(x) are given in Fig. below, for some polynomials p(x). Find the number of zeroes of p(x), in each case.

Solution :

The number of points where the graph cuts the x-axis gives the number of zeroes of any polynomial p(x).

The number of zeroes of p(x) is zero as the curve does not intersect the x-axis.

Question 1 (ii)

The graphs of y = p(x) are given in Fig. below, for some polynomials p(x). Find the number of zeroes of p(x), in each case.

Solution :

The number of points where the graph cuts the x-axis gives the number of zeroes of any polynomial p(x).

The number of zeroes is 1 as the graph cuts the x-axis at only one point.

Question 1 (iii)

The graphs of y = p(x) are given in Fig. below, for some polynomials p(x). Find the number of zeroes of p(x), in each case.

Solution :

The number of points where the graph cuts the x-axis gives the number of zeroes of any polynomial p(x).

The number of zeroes of p(x) is three as the graph intersects the x-axis thrice.

Question 1 (iv)

The graphs of y = p(x) are given in Fig. below, for some polynomials p(x). Find the number of zeroes of p(x), in each case.

Solution :

The number of points where the graph cuts the x-axis gives the number of zeroes of any polynomial p(x).

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

Question 1 (v)

The graphs of y = p(x) are given in Fig. below, for some polynomials p(x). Find the number of zeroes of p(x), in each case.

Solution :

The number of points where the graph cuts the x-axis gives the number of zeroes of any polynomial p(x).

The number of zeroes of p(x) is four as the graph intersects the x-axis four times.

Question 1 (vi)

The graphs of y = p(x) are given in Fig. below, for some polynomials p(x). Find the number of zeroes of p(x), in each case.

Solution :

The number of points where the graph cuts the x-axis gives the number of zeroes of any polynomial p(x).

The number of zeroes is 3 as the graph cuts the x-axis at 3 points.