If  $\alpha ,\beta (\alpha <\beta )$ are the roots of the equation $6x^2+11x+3=0.$ then which of the following are real?

  
Or  $6x^2+11x+3=0$
Or  $(2x+3)(3x+1)=0$

$x=-3/2,-1/3$
For $x=-3/2,{\cos }^{-1}x$  is not defined as domain of  ${\cos }^{-1}x$ is  $[-1,1]$ and  $x=-1/3,$$\cos e{c}^{-1}x$   is not defined as domain of $\cos e{c}^{-1}x$  is  $R-(-1,1).$ However,${\cot }^{-1}x$   defined for both of these values as domain of  ${\cot }^{-1}x$ is R