Let $f\left(x\right)=x^4+a{x}^3+b{x}^2+c$  be a polynomial with real coefficients such that $f\left(1\right)=-9$ . 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  $f\left(x\right)=0$,  then  $\frac{{\left|{\alpha }_1\right|}^2+{\left|{\alpha }_2\right|}^2+{\left|{\alpha }_3\right|}^2+{\left|{\alpha }_4\right|}^2}{4}$  is equal to ……  $[|a+ib|=\sqrt{a^2+b^2}wherea,b\in R\&\sqrt{-1}=i]$