y = x² + tx + t + 3
= x² + tx + t²/4 -t²/4 + t + 3
= (x + t/2)² -t²/4 + t + 3
要使y = x² + tx + t - 3恒大于0,则-t²/4 + t + 3 > 0即可
t² - 4t - 12 < 0
(t - 6)(t + 2) < 0
-2 < t < 6