A Perfect-Square Quartic

★ 6/10functions algebra Completing the Square Polynomials AM-GM

Problem

Let

f(x) = 4x^4 - 6tx^3 + (2t^2 + 6)x^2 - 3tx + 1, \qquad x > 0.

If the minimum value of $f(x)$ is $0$ , find $t$ .

Answer

Solution

Difficulty	6/10
Topics	functions, algebra, Completing the Square, Polynomials, AM-GM

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