The number of polynomials having zeroes as \(-2\) and \(5\) is
1
2
3
more than 3
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.