Q) If \( \alpha, \beta, \gamma \) and \( \delta \) be the roots \( Q \) the equation \( x^{4}+p x^{3}+q x^{2}+r x+s=0 \). Find (i) \( \Sigma \frac{\alpha}{\beta} \) (ii) \( \Sigma\left(\frac{\alpha \beta}{\gamma}\right. \) \( \begin{array}{ll}\text { (iii) } \Sigma\left(\frac{\alpha \beta}{\alpha}\right) & \text { (iv) } \Sigma \frac{\alpha^{2}}{\beta^{2}}\end{array} \)

16 Solve the system of equations using matrices. Use the Gaussian elimination method with back-substitution. \[ \begin{array}{r}x+y-z=-4 \\ 4 x-y+z=-1 \\ -x+5 y-4 z=1\end{array} \] The solution set is \( \{(\square, \square, \square)\} \). (Simplify your answers.)

1) A picture should be centered on a wall. The picture is 3 feet wide. The wall is 15 feet wide. How much space should be on the left \( (x) \) and right \( (x) \) of the picture? \( x+3+x=15 \) \( 2 x+3=15 \) What is the value of \( x \) ?

Find the least common denominator of \( \frac{2}{x-6} \) and \( \frac{7}{x+6} \)

16. Determine whether \( f(x)=8 x-1 \) is one-to-one. If it is, find a formula for its inverse.

Factor completely. \[ 5 v^{2}-30 v+70 \]