TR-MO-R1 2021 Problem 19

$a$ bir gerçel sayı olmak üzere, $x^3+ax^2+108=0$ denklemini sağlayan tam olarak iki farklı $x$ gerçel sayısı bulunmaktadır. Buna göre $a$ kaçtır?

a) $-6$ b) $-3$ c) 4 d) 8 e) Hiçbiri

Official text Turkish Mathematical Olympiad, first round 2021 official paper, page 10. Quoted with source.

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