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Let (x+10)⁵⁰ + (x-10)⁵⁰ = a₀ + a₁x + a₂x² + ⋯ + a₅₀x⁵⁰, for all x ∈ R; then (a₂)/(a₀) is equal to

1. 12.25
2. 12.75
3. 12.00
4. 12.50

Correct answer: 12.25

Solution

Expanding (x+10)^50 + (x-10)^50, odd powers cancel. a0 = 2*10^50 and a2 = 2*C(50,2)*10^48. So a2/a0 = C(50,2)/100 = 1225/100 = 12.25.

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