Sabendo que a equação x⁴ + 4 ⋅ x³ - 5 ⋅ x² + 8 ⋅ x + 2 = 0 possui raízes a, b, c e d. Assinale a alternativa que representa o polinômio cujas raízes são 3 ⋅ a, 3 ⋅ b, 3 ⋅ c e 3 ⋅ d:
Questão
Simulado EN
2024
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A
3 ⋅ x⁴ + 12 ⋅ x³ - 15 ⋅ x² + 24 ⋅ x + 6 = 0
B
x⁴ + 12 ⋅ x³ - 15 ⋅ x² + 24 ⋅ x + 6 = 0
C
x⁴ + 12 ⋅ x³ - 45 ⋅ x² + 216 ⋅ x + 162 = 0
D
x⁴ + 24 ⋅ x³ - 72 ⋅ x² + 32 ⋅ x + 18 = 0
E
2 ⋅ x⁴ + 18 ⋅ x³ - 12 ⋅ x² + 81 ⋅ x + 7 = 0