$\begin{align}  & \text{If the roots of the equation }{{x}^{2}}+7x+8=0\text{ are whose roots are }\alpha \text{ and }\beta ,\text{ } \\ & \text{Find the equation whose roots are }{{\alpha }^{2}}\text{ and }{{\beta }^{2}} \\\end{align}$ 

$\begin{align}  & \text{If }\alpha \text{ and }\beta \text{ are the roots of the equation }7+12x-7{{x}^{2}}=0,\text{ } \\ & \text{Find the equation whose roots are }\tfrac{\alpha }{\beta }\text{ and }\tfrac{\beta }{\alpha } \\\end{align}$

$\begin{align} & \text{If }\alpha \text{ and }\beta \text{ are roots of the equation }6{{x}^{2}}-10x+3=0,\text{ } \\ & \text{Find the value of } \\ & \text{(}i\text{) }{{(\alpha -\beta )}^{2}}\text{  } \\ & \text{(}ii\text{) }{{\alpha }^{2}}+{{\beta }^{2}}\text{  } \\ & \text{(}iii\text{) }({{\alpha }^{3}}+{{\beta }^{3}})\text{  } \\ & \text{(}iv\text{) }({{\alpha }^{3}}-{{\beta }^{3}})\text{  } \\ & \text{(}v\text{) }\tfrac{1}{\alpha }+\tfrac{1}{\beta } \\ & (vi)\text{ }\tfrac{1}{{{\alpha }^{2}}}+\tfrac{1}{{{B}^{2}}}\text{  } \\ & (vii)\text{ }\tfrac{\alpha }{\beta }+\tfrac{\beta }{\alpha } \\\end{align}$

$\begin{align}
& \text{The roots of the quadratic equation }a{{x}^{2}}+bx+c\text{ are }\alpha \text{ and }\beta ,\text{ those of }{{a}^{1}}{{x}^{2}}+{{b}^{1}}x+{{c}^{1}}=0\text{ are } \\
& \zeta \text{ and }\delta \text{. Find the equation whose roots }\left( \frac{\alpha }{\zeta }+\frac{\beta }{\beta } \right)\text{ and }\left( \frac{\alpha }{\delta }+\frac{\beta }{\zeta } \right) \\
\end{align}$