TR-MO-R1 2024 Problem 19

$r$ bir gerçel sayı olmak üzere, $5x^4 - 8x^3 + rx^2 - 11x + 10 = 0$ denkleminin gerçel köklerinin çarpımı 1 ise, gerçel köklerinin toplamı kaçtır?

a) $\dfrac{6}{5}$ b) 1 c) $\dfrac{4}{5}$ d) $\dfrac{3}{5}$ e) Hiçbiri

Official text Turkish Mathematical Olympiad, first round 2024 official paper, page 10. Quoted with source.

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