at 10:24 , in denominator [s+(alpha + beta)][s+(alpha - beta)] thana mam varanum, because if we simply that we get s^2 +(R/L)s + 1/LC.....but in your's [s-(alpha + beta)][s-(alpha - beta)].....
in the case i'm taking alpha = R/2L instead of -R/2L, Can i take alpha = R/2L an proceed mam? is there will be any problem?? i will change all equations with '+' sign..... eg like this [s+(alpha + beta)][s+(alpha - beta)]....