Let f:R→R is a polynomial function which satisfies f(x+y)+f(x-y)=2f(x)-2y2∀x,y∈R,f'(0)≠0 and f(0)=0 . Then which of the following is/are true

put x=0 in the given equation then f(y)+f(−y)=−2y2   since f0=0 andput y=x in the given equation then  f(2x)−2f(x)=−2x2f(x) must be quadratic f(x)=−x2+λx where λ=f1(0) area =∫0λ −x2+λxdx=λ36