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Polynomials CBSE NCERT Solutions
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.
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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