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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