Let $a$ be a constant. For the two functions in $x$

$$\begin{aligned}
& f ( x ) = 2 x ^ { 2 } + x + a - 2 \\
& g ( x ) = - 4 x - 5
\end{aligned}$$

we are to find the real values of $x$ for which $f ( x ) = g ( x )$ and also find the values of the two functions there.

(1) For each of $\mathbf { N } , \mathbf { O }$ and $\mathbf { P }$ in the following statements, choose the appropriate condition from (0) $\sim$ (8) below.

When $\mathbf { N }$, there are two real values of $x$ for which $f ( x ) = g ( x )$.
When $\mathbf { O }$, there is only one real value of $x$ for which $f ( x ) = g ( x )$.
When $\mathbf{P}$, there is no real value of $x$ for which $f ( x ) = g ( x )$.

(0) $a > \frac { 1 } { 8 }$\\
(1) $a = \frac { 17 } { 8 }$\\
(2) $a = \frac { 1 } { 6 }$\\
(3) $a < \frac { 1 } { 6 }$\\
(4) $a < \frac { 17 } { 8 }$\\
(5) $a < \frac { 1 } { 8 }$\\
(6) $a > \frac { 1 } { 6 }$\\
(7) $a = \frac { 1 } { 8 }$\\
(8) $a > \frac { 17 } { 8 }$

(2) When N, the values of $x$ for which $f ( x ) = g ( x )$ are $\frac { - \mathrm { Q } \pm \sqrt { \mathrm { R } - \mathbf { S } a } } { \mathbf{T} }$, and the values of the functions there are $\mp \sqrt { \mathbf { U } - \mathbf { V } a }$.

When O, the value of $x$ for which $f ( x ) = g ( x )$ is $- \frac { \mathrm { W } } { \mathrm { X} }$, and the value of the functions there is $\mathbf{Y}$.

(3) Consider the case where $f ( x ) = g ( x )$ and the absolute value of these functions there is greater than or equal to 3. The condition for this case is that $a \leqq - \mathbf { Z }$.