Given equation is f(x)=ax2+bx+c which satisfy, f(1)+2f(2)=0 ‌⇒‌‌a+b+c+2(4a+2b+c)=0 ‌⇒‌‌a+b+c+8a+4b+2c=0 ‌⇒‌‌9a+5b+3c=0......(i) ∴‌2f(1)+f(2)=0 ⇒‌‌2[a+b+c]+[4a+2b+c]=0 ‌6a+4b+3c=0.....(ii) Subtracting Eq (ii) from Eq. (i), we get 3a+b=0