A Polynomial with Integer Coefficients Having $\frac{3+\sqrt{3}}{7}$ As a Zero Is $f(x)=a x^{2}+b x+c$

Short Answer

A polynomial with integer coefficients having $\frac{3+\sqrt{3}}{7}$ as a zero is $f(x)=a x^{2}+b x+c$ , where $a=\ldots, b=\ldots$ , and $c=\ldots$ . Make your value for $a$ be positive and as small as possible.