Two rooks, because you can lose one and still be able to checkmate.
One Queen or Two Rooks?
[Date "12/17/2019 08:06PM"]
[FEN "r3k2r/pppppppp/8/8/8/8/PPPPPPPP/3QK3 w kq - 0 0"]
[White "Computer (Level 20) (0)"]
[Black "Computer (Level 20) (0)"]
1.d4 O-O 2.Qd3 b6 3.g4 e6 4.g5 d5 5.b4 c5 6.dxc5 bxc5 7.bxc5 Rfc8 8.Qa3 Rc7 9.f3 Rac8 10.Kf2 Rxc5 11.Qxa7 Rxc2 12.h4 g6 13.a4 Rd8 14.a5 Rcc8 15.Qe7 Re8 16.Qd7 Rcd8 17.Qc6 Rc8 18.Qb7 Rb8 19.Qd7 Rbd8 20.Qc6 Rc8 21.Qb7 Rb8 22.Qd7 Red8 23.Qe7 Re8 24.Qd7
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Imagine you are starting a game where both players get a single king, but your only additional pieces can be either one queen or two rooks. What would you choose? Your opponent gets whatever you don’t choose.