Eager
The abstract noun form for the adjective keen is keenness.
There is only one (1) syllable in the word keen.
blunt, pointless
Roy was very keen for apples today.
A knife is a keen tool that is dangerous for kids to play with.
Dull.
Yes it is
keen
The word 'keen' is a noun, a word for a dirge or a lament for the dead. Another noun form is 'keener', one who wails for the deadThe noun form for the adjective keen is keenness.
The word "keen" can mean sharp in the context of physical attributes, such as a keen blade or keen senses. It also conveys a sense of intensity or eagerness, such as having a keen interest or enthusiasm for something. In both cases, it suggests a heightened level of perception or ability.
That could be zeal or zest.
"Keen" is and adjective, used to describe something as sharp or acute. "The sword had a keen edge." "He was a man of keen intellect." It can also be used to express enthusiasm. "He was keen to learn another language."