Step-by-Step Solution
Key Concept: The family of polynomials with fixed zeroes $\alpha, \beta$ is $k(x - \alpha)(x - \beta)$ for any non-zero real constant $k$.
Stepwise Solution:
Polynomials are of the form $p(x) = k(x + 2)(x - 5)$ where $k \in \mathbb{R} \setminus \{0\}$. [0.5 Mark]
Since $k$ can take infinitely many real values, there are infinitely many (more than 3) such polynomials. [0.5 Mark]
Marking Scheme:
• Expressing polynomial family with constant $k$: 0.5 Mark
• Concluding infinitely many (more than 3): 0.5 Mark
Correct Answer: More than 3