Playing with Vieta

$f\left( x \right) ={ x }^{ 4 }+37{ x }^{ 3 }+71{ x }^{ 2 }+18x+3\\ \\ sum\quad of\quad coeff.\quad of\quad h\left( x \right) =h\left( 1 \right) \\ \\ h\left( 1 \right) =\left( 1-\cfrac { abcd }{ { d }^{ 2 } } \right) \left( 1-\cfrac { abcd }{ { c }^{ 2 } } \right) \left( 1-\cfrac { abcd }{ { b }^{ 2 } } \right) \left( 1-\cfrac { abcd }{ { a }^{ 2 } } \right) \\ \\ =\left( \cfrac { { d }^{ 2 }-3 }{ { d }^{ 2 } } \right) \left( \cfrac { { c }^{ 2 }-3 }{ { c }^{ 2 } } \right) \left( \cfrac { { b }^{ 2 }-3 }{ { b }^{ 2 } } \right) \left( \cfrac { { a }^{ 2 }-3 }{ { a }^{ 2 } } \right) \quad (as\quad abcd=3)\\ \\ =\cfrac { \left( { d }^{ 2 }-3 \right) \left( { c }^{ 2 }-3 \right) \left( { b }^{ 2 }-3 \right) \left( { a }^{ 2 }-3 \right) }{ 9 } \quad (as\quad { a }^{ 2 }{ b }^{ 2 }{ c }^{ 2 }{ d }^{ 2 }=9)\\ \\ =\cfrac { f\left( \sqrt { 3 } \right) .f\left( -\sqrt { 3 } \right) }{ 9 } \quad (\because \left( { a }^{ 2 }-3 \right) =\left( \sqrt { 3 } -a \right) \left( -\sqrt { 3 } -a \right) )\\ \\ =\cfrac { \left( 225+129\sqrt { 3 } \right) \left( 225-129\sqrt { 3 } \right) }{ 9 } =78$