Differentiation

Let $$f\left( x \right)$$ be a polynomial function of second degree. If $$f\left( 1 \right) = f\left( { - 1} \right)$$ and $$a,b,c$$ are in $$A.P,$$ then $$f'\left( a \right),f'\left( b \right),f'\left( c \right)$$ are in