The 2nd pattern F Major scale takes it’s root note positions from the A shape open chord. When looking at the open A chord the root notes are on the open 5th string and at the 2nd fret of the 3rd string.
A
Important: The notes used in the F Major scale are F, G, A, Bb, C, D, E, F, there is one flat in the F Major scale.
If we take a look at the scale on the fretboard, you will see something like the following pattern… the root notes are marked with the “X“
| | $3.7.$4.7.$5.7 | $1.8.$2.8.$4.8.$5.X.$6.8 | $3.9 | $1.10.$2.10.$3.X.$4.10.$5.10.$6.10 | $2.11 |
Note: In the diagram above it’s the fret numbers that are indicated not the scale degrees, and it isn’t the way you would normally write out a scale using TAB, it’s just to illustrate the fingering pattern of the scale. 
When playing this scale on the guitar, I normally start on the lowest pitch root note, the 8th fret A string with the middle finger, and play up to the highest pitch note of the scale, 1st string 10th fret, which is the D.
| $5.8 10 $4.7 8 10 $3.7 9 10 $2.8 10 11 $1.8 10 |
Descending back to the lowest pitch note of the scale, the C at the 8th fret bottom E string.
| $1.10 8 $2.11 10 8 $3.10 9 7 $4.10 8 7 $5.10 8 7 $6.10 8 |
Then back up in pitch to the F root note on the 8th fret A string.
| $6.8 10 $5.7 8 |