Polynomials 1

Algebra Level 5

A quadratic polynomial f(x)=x2+ax+bf\left( x \right) ={ x }^{ 2 }+ax+b is formed with one of its zeros being 4+332+3\frac { 4+3\sqrt { 3 } }{ 2+\sqrt { 3 } } where aa and bb are integers. Also g(x)=x4+2x310x2+4x10g\left( x \right) ={ x }^{ 4 }+{ 2x }^{ 3 }-{ 10x }^{ 2 }+4x-10 is a biquadratic polynomial such that g(4+332+3)=c3+dg\left( \frac { 4+3\sqrt { 3 } }{ 2+\sqrt { 3 } } \right) =\quad c\sqrt { 3 } +d where cc and dd are integers. Find the value of a+b+c+da+b+c+d.

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