The set of all values of $k > - 1$, for which the equation
$\left( 3 x ^ { 2 } + 4 x + 3 \right) ^ { 2 } - ( k + 1 ) \left( 3 x ^ { 2 } + 4 x + 3 \right) \left( 3 x ^ { 2 } + 4 x + 2 \right) + k \left( 3 x ^ { 2 } + 4 x + 2 \right) ^ { 2 } = 0$ has real roots, is:
(1) $\left[ - \frac { 1 } { 2 } , 1 \right)$
(2) $\left( 1 , \frac { 5 } { 2 } \right]$
(3) $\left( \frac { 1 } { 2 } , \frac { 3 } { 2 } \right] - \{ 1 \}$
(4) $[ 2,3 )$