NCERT solution class 10 chapter 2 polynomials

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.

 

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