The cubic equation [tex]x^{3}-kx^{2}-2=0[/tex] has roots [tex]\alpha , \beta[/tex] and [tex]\gamma.[/tex] [tex]\alpha[/tex] is real. [tex]\beta[/tex] is complex, and can be written in the form [tex]u+iv[/tex].

Find [tex]k[/tex] in terms of [tex]\alpha.[/tex]