+163 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.
