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 ?
Given that -LSB- math -RSB- \ alpha , \ beta -LSB- / math -RSB- are roots of the equation -LSB- math -RSB- 3x ^ 2-x-5 = 0 , -LSB- / math -RSB- can you find the equation whose roots are -LSB- math -RSB- \ frac -LCB- 2 \ alpha-1 -RCB- -LCB- \ beta -RCB- , \ frac -LCB- 2 \ alpha-1 -RCB- -LCB- \ alpha -RCB- -LSB- / math -RSB- ?