Question

x + p is a factor of both;
ax^2 + b and
ax^2 + bx − ac.
(i) Show that
p^2=-b/a and that p=-b-ac/b

(ii) Hence show that p^2 + p^3 = c

Answer 1

(I)- (x+p) is factor, therefor f(x) = 0 when x=-p(factor theorem).
So just sub in -p into each equation and rearrange till you get required result.
A(-p)^2+b=> p^2=-b/a
A(-p)^2 +b(-p) -ac => p=(-b-ac)/b

(ii) p^2 = -b/a, p=(-b-ac)/b
P^3= p x p^2
=> (-b-ac)/b + [(-b/a) x (-b-ac)/b] (this is p^2 + p^3)
Multiply out and simplify so it equals C