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Algebra Level 4

Let \(p\), \(q\) and \(r\) be the zeros of the polynomial \({ x }^{ 3 }+5{ x }^{ 2 }-4x+3\).

Find the value of \({ p }^{ 2 }q+{ p }^{ 2 }r+{ q }^{ 2 }p+r^{ 2 }p+{ q }^{ 2 }r+r^{ 2 }q\).

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