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min real root of 2x^5 + 5x^4 + 5x^3 + ax^2 + bx + c = 0, given all roots reals

Source: 2010 Thailand Mathematical Olympiad day 1 p9

March 12, 2021
polynomialalgebra

Problem Statement

Let a,b,ca, b, c be real numbers so that all roots of the equation 2x5+5x4+5x3+ax2+bx+c=02x^5 + 5x^4 + 5x^3 + ax^2 + bx + c = 0 are real. Find the smallest real root of the equation above.
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