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 $$a+b+c+d$$.