Question

Let g(x) a polynomial function with leading coefficient a and zeros 0, 1, 2, 3 and 4, then let f(x) = g(x) + x + 1. If f(5)=25, find a

Answer 1

g(x) = ax(x-1)(x-2)(x-3)(x-4)
f(x) = g(x) + x + 1

We are told: f(5) = 25
g(5) = 5a(4)(3)(2)(1) = 120a
f(5) = g(5) + 5 + 1 = 25
120a = 19
a = 19/120

Answer 2

a = 4