Let $a$ be a constant other than 0 . Let $$\begin{aligned}
& f ( x ) = x ^ { 2 } + 2 a x - 4 a - 12 , \\
& g ( x ) = a x ^ { 2 } + 2 x - 4 a + 4 .
\end{aligned}$$ (1) When the solutions of $f ( x ) = 0$ and the solutions of $g ( x ) = 0$ coincide, $a$ is $\mathbf { M N }$, and their solutions are $x = \mathbf { O P }$ and $x = \mathbf { Q }$. (2) $g ( x ) = 0$ has just one solution when $a = \frac { \mathbf { R } } { \mathbf { S } }$, and in this case the solution is $x =$ $\mathbf{TU}$. (3) The range of $a$ such that $f ( x ) < g ( x )$ for all $x$ is $\mathbf{VW}$.
Let $a$ be a constant other than 0 . Let
$$\begin{aligned}
& f ( x ) = x ^ { 2 } + 2 a x - 4 a - 12 , \\
& g ( x ) = a x ^ { 2 } + 2 x - 4 a + 4 .
\end{aligned}$$
(1) When the solutions of $f ( x ) = 0$ and the solutions of $g ( x ) = 0$ coincide, $a$ is $\mathbf { M N }$, and their solutions are $x = \mathbf { O P }$ and $x = \mathbf { Q }$.\\
(2) $g ( x ) = 0$ has just one solution when $a = \frac { \mathbf { R } } { \mathbf { S } }$, and in this case the solution is $x =$ $\mathbf{TU}$.\\
(3) The range of $a$ such that $f ( x ) < g ( x )$ for all $x$ is $\mathbf{VW}$.