Part CCSIR NET June 2025the-degree-2-condition-forces-a-squared-plus-b-squared-equals-6-and-hence-root-3

The degree 2 condition forces a squared plus b squared equals 6 and hence root 3

If $α, β \in R$ are such that the equation $\int_{0}^{3} f (x)$ dx $= (3/2) [f (α) + f (α + β)]$ holds for all polynomials f(x) of degree less than or equal to 2, then which of the following statements are true?

A. $(α, β) = ((3 - 3) /2, 3)$ or $(α, β) = ((3 + 3) /2, - 3)$ ✓
B. $(α, β) = ((3 - 2) /2, 2)$ or $(α, β) = ((3 + 2) /2, - 2)$
C. $(α, β) = ((3 - 5) /2, 5)$ or $(α, β) = ((3 + 5) /2, - 5)$
D. $(α, β) = ((3 - 7) /2, 7)$ or $(α, β) = ((3 + 7) /2, - 7)$

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, and why this one tests execution slip.

See pricing

50 are analysed free — try those first.

The trap it tests

Execution slip

The idea was right. The computation was not.

Drill statements like this

The degree 2 condition forces a squared plus b squared equals 6 and hence root 3

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