The characteristic equation for a recurrence relation is (x – 3)(x - 2)²(x + 5) = 0. What is the general solution for the recurrence relation?
a) fₙ = a₁ ∙ 3ⁿ + a₂ ∙ 2ⁿ + a₃ ∙ n2ⁿ + a₄ ∙ (-5)ⁿ
b) fₙ = a₁ ∙ 3ⁿ + a₂ ∙ 2ⁿ + a₃ ∙ 2ⁿ - a₄ ∙ 5ⁿ
c) fₙ = a₁ ∙ 3ⁿ + a₂ ∙ 2ⁿ + a₃ ∙ 2ⁿ - a₄ ∙ (-5)ⁿ
d) fₙ = a₁ ∙ 3ⁿ + a₂ ∙ 2ⁿ + a₃ ∙ n2ⁿ - a₄ ∙ 5ⁿ