Answer:
p=3 and q = 6
Step-by-step explanation:
f(x) = px (q-x) = pxq -x²p
f(x) = -px² + pqx
you have the system : f(6) = 0........(*)
f(3) = 27.....(**)
(*) means : when x =6 y = 0 : -p(6)² + pq(6) = 0 .... -36p +6pq =0
(**) means : when x =3 y = 27 : -p(3)² +pq(3) = 27........ -9p +3pq = 27
so the system : -6p +pq =0...(1)
-3p +pq = 9 ...(2)
by (1) : pq = 6p
by(2) : pq = 3p +9
so : 6p =3p+9
3p = 9
p=3 put this value in (1) : -6(3)+3q =0
3q =18
q=6 so : f(x) = -3x²+18x
*PICTURE ATTACHED*
