‌f′(x)=ax4+bx3+cx2+dx+e ‌f′(4)=0,f(5)=0 Also
lim
x⟶0
‌
f(x)
x2
=5 ⇒
lim
x⟶0
(‌
ax4+bx3+cx2+dx+e
x2
)=5 ⇒d=e=0 and c=5 ‌∴f(x)=ax4+bx3+5x2 ‌f′(x)=4ax3+3bx2+10x ‌f′(4)=256a+48b+40=0.....(i) ‌f′(5)=500a+75b+50=0.......(ii) Solving equation (i) and (ii) ‌‌ We get ‌a=‌