If $x^2+\lambda x+1=0, \lambda$ is part of $(-2,2)$ and $4x^3+3x+2c=0$ have common root then $c+\lambda$ can be 
If $x^2+\lambda x+1=0, \lambda$ is part of $(-2,2)$ and $4x^3+3x+2c=0$ have common root then $c+\lambda$ can be      

I can't figure out a way to solve this question. A hint would be great.

If $\lambda$ is in $(-2,2)$ (not to be confused with $[-2,2]$), then the roots of $x^2+\lambda x+1=0$ are complex because $x^2+\lambda x +1=0$ only has real solutions when $\lambda=2$ and $\lambda = -2$.
Let $a$ be a shared solution of $x^2+\lambda x+1=0$ and $4x^3+3x+2c=0$. Since $a$ is complex, $4a^3+3a+2c=0$ gives us $c=-\frac{4a^3+3a}{2}$. Thus, $c$ is complex, so $\lambda + c$ is complex.
