Equal Values of a Cubic

★ 5/10functions algebra Polynomials Vieta's Formulas Discriminant

Problem

Let $f(x) = x^3 + (a+2)x^2 + bx + c$ with $a, b, c \in \mathbb{R}$ . Suppose there exist real numbers $m$ and $n$ , distinct from each other and both different from $a$ , such that

f(m) = f(n) = f(a).

Find the set of all possible values of $b$ .

Answer

Solution

Difficulty	5/10
Topics	functions, algebra, Polynomials, Vieta's Formulas, Discriminant

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