MathDB

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Part of 2009 Grand Duchy of Lithuania

Problems(1)

2b^3+ 9a^2 d - 7abc <= 0 for f(x) = ax^3 + bx^2 + cx + d, f(0) < 0

Source: 2009 Grand Duchy of Lithuania, Mathematical Contest p2 (Baltic Way TST)

10/3/2020
Let f(x)=ax3+bx2+cx+df(x) = ax^3 + bx^2 + cx + d be a polynomial with real coefficients. Given that f(x)f(x) has three real positive roots and that f(0)<0f(0) < 0, prove that 2b3+9a2d−7abc≤02b^3+ 9a^2 d - 7abc \le 0.
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