Milestone: 100,000 points! (An excuse to post a problem)

Algebra Level 5

\[\large f(x) = 16x^4+96x^3+224x^2+240x+40p-4p^2\]

If \(p \) is a real constant in the interval satisfying \(a<p<b\) such that \(f(x) \) has no real roots, find \(a+b\).

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