Consider the Fibonacci sequence defined by \( F_1 = 1 \), \( F_2 = 1 \), and \( F_n = F_{n-1} + F_{n-2} \) for \( n \geq 3 \). Find the sum of the roots of the quadratic equation \( x^2 - 8x + 15 = 0 \) and explain how this relates to the Fibonacci sequence. Let's think step by step and output the final answer within \boxed{}.
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