If we have a multi-tap transformer like this:
Is it possible to use two of the taps to generate negative voltage and use other taps for positive voltage?
Is it possible to use two of the taps to generate negative voltage and use other taps for positive voltage?
Not that way.
Figure 1. The common GND on the two rectifier outputs places a short-circuit on the transformer via two rectifier diodes.
simulate this circuit – Schematic created using CircuitLab
Figure 2. Two standard ways to do it. (a) Half-wave rectification. (b) Bridge rectification.
Relative to the lower tap on the secondary marked with a "0" (the reference node), all other taps will produce positive and negative half cycles of voltage and, with the appropriate diode arrangement (plus smoothing capacitors), all other taps can be used to create negative and positive DC voltages.
Is it possible to use two of the taps to generate negative voltage and use other taps for positive voltage?
You can use the same (or different) taps to generate positive and negative voltages because each tap produces positive and negative half cycles that can be rectified into positive and negative DC voltages.