Use the Newton-raphson method or you can use your own iterative method...but doing it the latter way may fail to converge to a root N-R form: [tex]\alpha_{n+1}=\alpha_n -\frac{f(\alpha_n)}{f'(\alpha_n)}[/tex]
Buit the crucial point is YOUR method. Whatever method you use, YOU are supposed to do it. Have you tried using Newton-Raphson? This is, I think, now the fourth problem you have posted with no sign of attempting it yourself.