Given that \(p = \begin{bmatrix} x&4\\3&7\end{bmatrix} Q =\begin{bmatrix} x&3\\1&2x\end{bmatrix}\) and the determinant of \(Q\) is three more than that of \(P\) , find the values of \(x\)

A.

\(-2,\frac{3}{2}\)

B.

\(2,\frac{3}{2}\)

C.

\(-2,-\frac{3}{2}\)

D.

\(2-,\frac{3}{2}\)

Correct answer is B

\(p = \begin{bmatrix} x&4\\3&7\end{bmatrix}, Q =\begin{bmatrix} x&3\\1&2x\end{bmatrix}\)

\(p = \begin{bmatrix} x&4\\3&7\end{bmatrix}=7x-12, Q =\begin{bmatrix} x&3\\1&2x\end{bmatrix}=2x^2-3\)

|Q| = |P| + 3 (Given)