Solve the following quadratic equations by completing the square method
9x² - 12x + 4 = 0

If the difference between a number and its reciprocal is \(\frac {24}{5}\), find the number.

Determine the nature of roots for the following quadratic equations
x² - x - 20 = 0

If α, β are the roots of 7x² + ax + 2 = 0 and if β - α = \(\frac {-13}{7}\). Find the values of a.

If one root of the equation 3x² + kx + 81 = 0 (having real roots) is the square of the other then find k.

Consider the following information regarding the number of men and women workers in three factories I, II and III.

Factory	Men	Women
I	23	18
II	47	36
III	15	16

Represent the above information in the form of a matrix. What does the entry in the second row and first column represent?

If A = \(\left[ \begin{matrix} \sqrt { 7 } & -3 \\ -\sqrt { 5 } & 2 \\ \sqrt { 3 } & -5 \end{matrix} \right] \) then find the transpose of -A.

If A = \(\left[ \begin{matrix} 1 & 3 & -2 \\ 5 & -4 & 6 \\ -3 & 2 & 9 \end{matrix} \right] \), B = \(\left[ \begin{matrix} 1 & 8 \\ 3 & 4 \\ 9 & 6 \end{matrix} \right] \), find A + B.

If A = \(\left[ \begin{matrix} 7 & 8 & 6 \\ 1 & 3 & 9 \\ -4 & 3 & -1 \end{matrix} \right] \), B = \(\left[ \begin{matrix} 4 & 11 & -3 \\ -1 & 2 & 4 \\ 7 & 5 & 0 \end{matrix} \right] \) then Find 2A + B.

If A = \(\left[ \begin{matrix} 5 & 4 & -2 \\ \frac { 1 }{ 2 } & \frac { 3 }{ 4 } & \sqrt { 2 } \\ 1 & 9 & 4 \end{matrix} \right] \), B = \(\left[ \begin{matrix} -7 & 4 & -3 \\ \frac { 1 }{ 4 } & \frac { 7 }{ 2 } & 3 \\ 5 & -6 & 9 \end{matrix} \right] \), find 4A - 3B.