# Half way squared polynomials

Algebra Level 5

If $$P(x)=x^{3}-3x^{2}+2x+5$$ and $$a_{1}, a_{2}, a_{3}$$are roots of $$P(x)$$, then find the sum of the coefficients of a monic polynomial whose roots are $$(a_{1})^{2}a_{2}a_{3},(a_{2})^{2}a_{1}a_{3},(a_{3})^{2}a_{2}a_{1}$$.

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