Polynomials 1

Algebra Level 5

A quadratic polynomial \(f\left( x \right) ={ x }^{ 2 }+ax+b\) is formed with one of its zeros being \(\frac { 4+3\sqrt { 3 } }{ 2+\sqrt { 3 } } \) where \(a\) and \(b\) are integers. Also \(g\left( x \right) ={ x }^{ 4 }+{ 2x }^{ 3 }-{ 10x }^{ 2 }+4x-10\) is a biquadratic polynomial such that \(g\left( \frac { 4+3\sqrt { 3 } }{ 2+\sqrt { 3 } } \right) =\quad c\sqrt { 3 } +d\) where \(c\) and \(d\) are integers. Find the value of \(a+b+c+d\).

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