(k+1)x-2kx+k+4=0
kx+x-2kx+k+4=0
(x-2kx+k)+kx+4=0
(x-k)+kx+4=0
因(x-k)≥0
kx≥0
所以(x-k)+kx+4≥4
故(k+1)x-2kx+k+4=0无根.