A Polynomial Problem with Vieta's Rules

Algebra Level 4

\[ r_2 r_3 r_4 r_5 + r_1 r_3 r_4 r_5 + r_1 r_2 r_4 r_5 + r_1 r_2 r_3 r_5 + r_1 r_2 r_3 r_4 \]

Let the roots of \(P(x) = 4x^5 - 13x^3 - 12x+7\) be \(r_1, r_2, r_3, r_4\) and \(r_5\), then find the value of the expression above.

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