Mathematics - Quadratic Equation Question with Solution | TestHub

Let $f(x)=x^4+a{x}^3+b{x}^2+c$ be a polynomial with real coefficients such that $f(1)=-9$. Suppose that $i\sqrt{3}$ is a root of the equation $4x^3+3a{x}^2+2bx=0$, where $i=\sqrt{-1}$. If ${\alpha }_1,{\alpha }_2,{\alpha }_3$, and ${\alpha }_4$ are all the roots of the equation $f(x)=0$, then ${\left|{\alpha }_1\right|}^2+{\left|{\alpha }_2\right|}^2+{\left|{\alpha }_3\right|}^2+{\left|{\alpha }_4\right|}^2$ is equal to ________.