and the maximum value attained by f is 18.
since 1 is a root of , we can write
; p being the other root.
given that , we have .
also maximum value of is 18 and we know that the maxima occurs at as p and 1 are the roots of f, we have
, which simplifies to,
. now multiply both sides by k to get,
. we already have the value of which is 10, so we have,
which gives two values of k which are . both are acceptable as k had to be negative( if k is not negative then maxima of f does not exist).
corresponding values of p are -5 and -0.2.
so we have two such quadratic functions which can be found out by putting the values of k and p in