Descriptors and Energy damage

[Rhuan]

Let's say im casting a:

1 - Normal Fireball, it deal fire damage and has the fire descriptor

2 - Half Cold Half Fire, Fireball with the Elemental spell (Metamagic) feat, It deals 50% fire and 50% cold damage and carries Both fire and Cold descriptors

3 - Full cold damage Fireball with the Elemental Spell (Metamagic) Feat, it deals cold damage and has Fire and Cold descriptor or only the cold descriptor?

Elemental Spell (Metamagic):

You can manipulate the elemental nature of your spells.

Benefit: Choose one energy type: acid, cold, electricity, or fire. You may replace a spell’s normal damage with that energy type or split the spell’s damage, so that half is of that energy type and half is of its normal type.

Level Increase: +1 (an elemental spell uses up a spell slot one level higher than the spell’s actual level.)

Special: You can gain this feat multiple times. Each time you must choose a different energy type.

The feat doenst say the spell loses the old descriptor even when you fully replaces the damage with a new one. Another exemple here:

Benthic Spell (Metamagic):

Explorers in the depths of the Arcadian Ocean have learned that deadly pressure can be just as lethal as any flame.

Benefit: You can modify a spell that deals acid, cold, electricity, or fire damage to deal damage through high-pressure water instead. The spell gains the water descriptor, and you can either replace the spell’s normal damage with bludgeoning damage or split the spell’s damage so that half is bludgeoning and half is of its normal type. Creatures with damage reduction apply their damage reduction to bludgeoning damage from a benthic spell, but the spell counts as bludgeoning and magic for the purposes of bypassing damage reduction.

A benthic spell uses up a spell slot one level higher than the spell’s actual level.

[Bob Bob Bob]

Elemental Spell doesn't modify the descriptors in any way (if what you quoted is correct). A half cold half fire Fireball only has the [fire] descriptor. An all cold Fireball still only has the [fire] descriptor, even though it doesn't do any fire damage. A spell neither loses nor gains any descriptors from Elemental Spell.