We consider the system given by the following augmented matrix \( \left[\begin{array}{rrr|r}1 & -2 & 1 & 4 \\ 0 & 1 & -1 & 3 \\ 0 & 0 & \alpha^{2}-\alpha-2 & \alpha+1\end{array}\right] \) Determine the value (s) of \( \alpha \) for which the system has exactly one solution. None of the given options are correct \( \alpha \neq-1 \) \( \alpha \in(-\infty, 1) \cup(1, \infty) \) \( \alpha \) is any real number \( \alpha \in(-\infty, 2) \cup(2, \infty) \) a

The function \( f(x)=2 x^{2}-5 x+2 k-1 \) does not intersect the \( x- \) axis. Find the range of values of \( k \)

Which expression is equivalent to \(( x^ { \frac { 3} { 7} } ) ^ { 2} \) ?A. \(x^ { \frac { 6} { 14} } \)B. \(x^ { \frac { 17} { 7} } \)C. \(x^ { \frac { 6} { 7} } \)D. \(x^ { \frac { 5} { 7} } \)

Solve the system of quadratic inequalities: \[ \begin{array}{l}y<x^{2}-4 \\ y>-x^{2}+2\end{array} \]

The polynomial of degree \( 4, P(x) \), has a root of multiplicity 2 at \( x=3 \) and roots of multiplicity 1 at \( x=0 \) and \( x=-1 \). It goes through the point \( (5,12) \). Find a formula for \( P(x) \). \( P(x)=\square \)

Solve the system of quadratic inequalities: \[ \begin{array}{c}\mathrm{y}>\mathrm{x}^{2}-1 \\ \mathrm{y} \leq-\frac{1}{3} \mathrm{x}^{2}+5\end{array} \]