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Algebra Level 4

Let pp, qq and rr be the zeros of the polynomial x3+5x24x+3{ x }^{ 3 }+5{ x }^{ 2 }-4x+3.

Find the value of p2q+p2r+q2p+r2p+q2r+r2q{ p }^{ 2 }q+{ p }^{ 2 }r+{ q }^{ 2 }p+r^{ 2 }p+{ q }^{ 2 }r+r^{ 2 }q.

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