A Polynomial Problem with Vieta's Rules

Algebra Level 4

r2r3r4r5+r1r3r4r5+r1r2r4r5+r1r2r3r5+r1r2r3r4 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)=4x513x312x+7P(x) = 4x^5 - 13x^3 - 12x+7 be r1,r2,r3,r4r_1, r_2, r_3, r_4 and r5r_5, then find the value of the expression above.

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