given that y=2x^2 + px +16 and that y < 0 only when 2 < x < k, find the value of p and of k
y = 2x^2 + px + 16
This curve is a U shaped curve with its roots at 2 and k respectively.
Using Remainder and Factor Theorem
let f(x) = 2x^2 + px + 16
f(2) = 0, f(k) = 0
8 + 2p + 16 = 0
24 + 2p = 0
p = -12
2k^2 - 12k + 16 = 0
k^2 - 6k + 8 = 0
(k - 2)(k - 4) = 0
k = 2 or k = 4
k = 2 is rejected since k must be bigger than 2.
Therefore, k = 4, p = -12