It is a common error to pronounce discover with a long o sound. The word ‘over’ does have a long o sound like in the word ‘oh’ . But the first vowel in the word ‘discover’ has a soft sound like the ‘u’ in the words ‘love’ an ‘of’.
You can listen to the pronunciation at www.m-w.com.
Similarly another, cover, other, brother, hover all have the short vowel sound heard in ‘up’ .
Clover and Rover have a long o sound like in the word ‘over’.
I hope you like it!
Mary from USA