Part CCSIR NET December 2024two-conditions-determine-the-pair

Two conditions determine the pair

If $λ \in R$ and $p \in R$ are such that the quadrature formula $\int_{(} x_{0})^{(} x_{0} + h) f (x)$ dx $\approx λ h (f (x_{0}) + f (x_{0} + h)) +$ ph $^{3} (f^{''} (x_{0}) + f^{''} (x_{0} + h))$ is exact for all polynomials of degree as high as possible, then

A. $2 λ + 24 p = 0$ ✓
B. $7 λ - 12 p = 4$ ✓
C. $2 λ + 24 p = - 3$
D. $7 λ - 12 p = 11$

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

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Two conditions determine the pair

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