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The polynomial \(f(x) = x^3 +x^2 +2x+3\) has three distinct roots. Let  \(g(x) = x^3 +bx^2 +cx+d\) be a cubic polynomial with leading coefficient 1 such that the roots of \(g(x)\) are the squares of the roots of \(f(x)\). Find the ordered triple \((b,c,d)\).

Thanks in advance.

 Jul 27, 2020
 #1
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Like so:

 

Make sure you check this carefully to see if I've made any silly mistakes!

 Jul 27, 2020
 #2
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f1.f2.f3. = -3 ?

Guest Jul 27, 2020
 #3
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Oops!  Quite right.  I messed up that detail.  The method still holds but Firebolt will need to go through it correcting the numerics.

Alan  Jul 27, 2020

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