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Polynomials
RD Sharma
CBSE
Grade 10
Question:
The number of polynomials having zeroes as $-2$ and $5$ is: (a) $1$ (b) $2$ (c) $3$ (d) More than $3$
Step-by-Step Solution
Key Concept: Family of polynomials $k(x^2 - 3x - 10)$ for any non-zero real $k$.
Polynomial is of form $k(x + 2)(x - 5)$ where $k \in \mathbb{R} \setminus \{0\}$. Since infinitely many values of $k$ exist, the number of polynomials is more than 3. [1.0 Mark]
--- 🎯 Official CBSE Marking Scheme: Deducing infinitely many polynomials for non-zero scalar $k$: 1.0 Mark
Correct Answer:More than $3$
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