# 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.

×