Q1 of 64 Page 38

Find the number of zeros of the following polynomials:

p(x) = x3 — x

Here, p(x) = x3 — x


To find the zeros of p(x), consider p(x) = 0


∴ x3 – x = 0


∴ x (x2 – 1) = 0


∴ x (x – 1) (x + 1) = 0 Using the identity: (a2 – b2) = (a – b) (a + b)


∴ x = 0 or x = –1 or x = 1


∴ 0, –1 and 1 are the zeros of p(x).


Thus, the number of zeros of the given polynomial is 3.


More from this chapter

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1

Find the number of zeros of the following polynomials:

p(x) = x —x2 —1

 1

Find the number of zeros of the following polynomials:

P(x) = 3x —2

 2

Find the number of zeros and real zeros of p(x) = x3 + 1. Show them by a graph.

 3

Draw the graph of p(x) = x2 + 1 and find the real zeros of this polynomial.