Chapter 2: Polynomials

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Polynomials CBSE NCERT Solutions

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.

Answer:

Solutions:  We know that a polynomial p(x) of degree n, the graph of y = p(x) intersects the x-axis at most n points. Therefore, a polynomial p(x) of degree n has at most n zeroes.

 

(i) The graph of P(x) does not intersect the x-axis as shown, so there are no zeros in p(x).

                                          


(ii) The graph of P(x)  intersects the x-axis in one place as shown, so there is one zero in p(x).

(iii) The graph of P(x) intersects the x-axis at three places as shown, so there are three zeros in p(x).


(iv) The graph of P(x) intersects the x-axis at two places as shown, so there are two zeros in p(x).



(v) The graph of P(x) intersects the x-axis at four places as shown, so there are four zeros in p(x).


(vi) The graph of P(x) intersects the x-axis at three places as shown, so there are three zeros in p(x).


                   

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