Question:medium
Let \( S = \{x^3 + ax^2 + bx + c : a, b, c \in \mathbb{N} \text{ and } a, b, c \le 20\} \) be a set of polynomials. Then the number of polynomials in \( S \), which are divisible by \( x^2 + 2 \), is:
Let \( S = \{x^3 + ax^2 + bx + c : a, b, c \in \mathbb{N} \text{ and } a, b, c \le 20\} \) be a set of polynomials. Then the number of polynomials in \( S \), which are divisible by \( x^2 + 2 \), is:
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When checking divisibility of polynomials, always equate coefficients after expansion and then apply the given bounds carefully.
Updated On: Apr 1, 2026
- \(120\)
- \(10\)
- \(20\)
- \(6\)
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The Correct Option is B
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