Coefficient of highest degree term must be negative becuase if it is positive, then x → ∞, y → ∞ and it is not possible, since f(x) ≤ 100.
Now, graph will be like
at least two real roots will be there, & if
x≠, then f(x) < 100, it is not always true, as the graph can be like this also
Now, let the highest coefficients, it can have is 49
then,
f()=49+++...But the sum cannot be equal to 100.