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Let a be the sum of all coefficients in the expansion of (1–2x + 2x 2 ) 2023 (3 – 4x 2 + 2x 3 ) 2024 and b = ( ) . x dt 1 t t 1 log lim 2 x 0 2024 0 x ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ + + ∫ → If the equations cx 2 + dx + e = 0 and 2bx 2 + ax + 4 = 0 have a common root, where c, d, e ∈ R, then d: c: e equal

1. 1 : 1 : 4
2. 4 : 1 : 4
3. 2 : 1 : 4
4. 1 : 2 : 4

Correct answer: 1 : 1 : 4

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