7. Determine the quadratic polynomial for the given roots

If \(\alpha\) and \(\beta\) are zeroes of the polynomial \(x^2 + 4x + 7\), determine the polynomial whose zeroes are \(1+ \frac{\beta}{\alpha}\) and \(1 + \frac{\alpha}{\beta}\).

 

The required quadratic polynomial is $i{i}^i-ii+i$.