Stuck with this Question based on/related to Vieta's Relations.

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Nov 2019
1
0
India
If p , q, r are the roots of \(\displaystyle x^3-6x^2+3x+1=0,\)
determine the possible values of \(\displaystyle p^2q+q^2r+r^2p.\)
Also find \(\displaystyle |(p-q)(q-r)(r-p)|.\)20191126_182500.jpg20191126_182804.jpg


I have attached the pictures of my attempt.

I need 1 more equation of the terms to find the solution.

Answer :– -3, 24
 
Jun 2013
1,112
590
Lebanon
\(\displaystyle (y-x)^2\) is a symmetric expression (it is the discriminant of the polynomial)

therefore it can be expressed in terms of elementary symmetric polynomials.

Its value is \(\displaystyle 729\), so \(\displaystyle |y-x|=27\)