Let a b be constants Show that if ax2bcosx0 for all x then a

Let a, b be constants. Show that if

ax^2+bcosx=0 for all x then a=0 and b=0.

Then find constant a and b such that

ax^2+5cosx=2x^2+bcosx

Solution

given ax^2+5cosx=2x^2+bcosx

by comparing ax^2+5cosx with 2x^2+bcosx

we get a=2,b=5

therefore a=2,b=5