For how many positive integer values of $k$ does $kx^2+10x+k=0$ have rational solutions?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
For how many positive integer values of $k$ does $kx^2+10x+k=0$ have rational solutions?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
3
For how many positive integer values of $k$ does $kx^2+10x+k=0$ have rational solutions?
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