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Let \(r_1, r_2, \dots r_7\) be the roots of \(f(x) = x^7 + 5x^5 - 4x^4 + 5x^3 - 9x^2 + x + a,\) where \(a\) is some real constant.

 

Let \(g(x) = x^3 + 3x - 3.\) Then the product \(g(r_1) g(r_2) \dotsm g(r_7)\) can be expressed as a polynomial in \(a.\) Find this polynomial.

 

Any help or ideas appreciated!!!

(Reposting because the prior answer was wrong.)

 Feb 25, 2022
 #1
avatar+117232 
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Please include the address of the original question.

 Feb 26, 2022
 #2
avatar+117232 
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Beats me ... any ideas.

 Feb 26, 2022
edited by Melody  Feb 26, 2022

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