Exercise 2.1

Question 1

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

(i)

Sol :

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

(ii)

Sol :

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

(iii)

Sol :

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

(iv)

Sol :

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

(v)

Sol :

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

(vi)

Sol :

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

**Concept insight: **Since the polynomial p(x) given here is a polynomial in variable x, so to find the number of zeroes, we look at the number of points where the graph intersects or touches the x-axis and not the y-axis.

At all these points where the graph intersects x axis the value of the polynomial y = p(x) will be zero.