NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 2: Polynomials - Exercise 2.1

Question 4

Step 1: If \(-2\) and \(5\) are the zeroes of a polynomial, then the factorised form of such a polynomial must include \((x + 2)(x - 5)\).

Step 2: For example, one polynomial is

\(p(x) = (x + 2)(x - 5)\).

Step 3: But multiplying this expression by any non-zero constant also gives a valid polynomial with the same zeroes. For instance:

\(q(x) = 2(x + 2)(x - 5)\),

\(r(x) = -3(x + 2)(x - 5)\),

\(s(x) = 10(x + 2)(x - 5)\),

and so on.

Step 4: All of these have the same zeroes \(-2\) and \(5\), because the constant multiple does not affect the roots.

Conclusion: There are infinitely many such polynomials. Therefore, the correct choice is (D) more than 3.