Question

Let \( u+v+w=3 \), \( u,v,w \in \mathbb{R} \) and \( f(x)=ux^2+vx+w \) be such that \[ f(x+y)=f(x)+f(y)+xy,\quad \forall x,y \in \mathbb{R}. \] Then \( f(1) \) equals:

• A. \( \frac{5}{2} \)
• B. \( \frac{1}{2} \)
• C. \( \frac{1}{\sqrt{2}} \)
• D. \( 3 \)

Hint:

For quadratic functional equations: Expand both sides fully. Match coefficients term-by-term.

Answer 1

The Correct Option is B