how to form a quadratic equation If $\alpha$ and  $\beta$ are the root of the equation  $x^2 - 4x +6 =0$ , find the equation whose roots are $\alpha + 1/\beta$ and $\beta + 1/\alpha$.

$x^2 - \frac{28}{6}x + \frac{49}{6}$.
$\alpha + \beta = 4$ and $\alpha\beta = 6$. Expand $(x - (\alpha + \frac{1}{\beta}))(x-(\beta + \frac{1}{\alpha}))$. This gives us $x^2 - (\alpha + \beta)(1 + \frac{1}{\alpha\beta})x + (\alpha\beta + 2 + \frac{1}{\alpha\beta})$ So, doing the necessary substitutions gives us: $x^2 - (4\times \frac{7}{6}) x + (6 + 2 + \frac{1}{6})$ which is equal to $x^2 - \frac{28}{6}x + \frac{49}{6}$  
