Pinning a Cubic Combination

★ 6/10functions algebra Polynomials Vieta's Formulas

Problem

Let $f(x) = ax^3 + bx^2 + cx + d$ with $a, b, c, d \in \mathbb{R}$ and $a \neq 0$ . If

0 < 2f(2) = 3f(3) = 4f(4) < 1,

find the range of possible values of $f(1) + f(5)$ .

Answer

Solution

Difficulty	6/10
Topics	functions, algebra, Polynomials, Vieta's Formulas

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