Are you good at manipulating?

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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