How to resize an image to fit A4 when printing without loss of quality

[frozensun]

Ok guys,I did some screen caps (print screen) with resolution of 2764x1215 and when I print the image it doesn’t print over full sized A4 paper.
I even did scale to fit media in Photoshop which just increases DPI and basically I get print out over center of the paper,it’s not bad but letters are small,same like images.
Although quality is okay above 200 dpi.
I need printout to 1754x1240 and that one perfectly fits to A4,but I can’t screen capture at that resolution because I don’t own 4K monitor like the guy who sent me the image does.
There is an option in my printer to fit to page but when I choose it,image kinda streches all over A4 and the picture looks pretty bad.
What can I do to print kinda decent over A4 paper with not loss in quality?
A guy who wanted me for this did it with resolution of 1754x1240 I did print his image and it looks great,over full sized A4.
Can't I resize to that resolution,add custom width and height and print that image on A4 without loss of quality?

 

[hankscorpio]

Screencaptures depend on the display resolution, the higher your display resolution, the higher the quality of the screen capture.

You can't increase the size of a bitmap image without reducing the amount of dots per inch.
For example, if you have a square that's 1 inch x 1 inch and it has 300 dots in it - it has 300 dots per inch.
If you increase this to 2 inches x 2 inches - you still have 300 dots - but now there are only 150 dots per inch.

So - no, you can't take a small image and increase it in size and keep the same image.
The only way is with a better original sample.

And for screenshots you need a higher display resolution to get a better screen capture.