If alpha,betainmathbb R are such that the equation int0^3f(x),dx=frac32[f(alpha)+f(alpha+beta)] holds for all polynomials f(x) of degree less than or equal to 2, then which of the following statements are true?

Q97Section C (Part C)97 of 120

Two-point Gauss rule on $[0,3]$

If $\alpha,\beta\in\mathbb R$ are such that the equation

$\int_0^3f(x)\,dx=\frac32\big[f(\alpha)+f(\alpha+\beta)\big]$

holds for all polynomials $f(x)$ of degree less than or equal to $2$ , then which of the following statements are true?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Select every correct option, then submit.

Keyboard: A–D answer · S solution · ←/→ previous/next