If -LSB- math -RSB- \ alpha -LSB- / math -RSB- and -LSB- math -RSB- \ beta -LSB- / math -RSB- are roots of equation -LSB- math -RSB- x ^ 2-2px +2 p ^ 4 -LSB- / math -RSB- , then what is the maximum value of -LSB- math -RSB- \ alpha ^ 2 + \ beta ^ 2 -LSB- / math -RSB- ?
The roots of the equation -LSB- math -RSB- x ^ 2 +3 x-10 = 0 -LSB- / math -RSB- are -LSB- math -RSB- \ alpha -LSB- / math -RSB- and -LSB- math -RSB- \ beta -LSB- / math -RSB- , where -LSB- math -RSB- \ alpha < \ beta -LSB- / math -RSB- . An equation whose roots are -LSB- math -RSB- \ alpha-1 -LSB- / math -RSB- and -LSB- math -RSB- \ beta +2 -LSB- / math -RSB- is ?