Question

對(duì)?x∈R，kx²-kx-1＜0是真命題，則k的取值范圍是________．

Answer 1

-4＜k≤0
分析：對(duì)k=0與k＜0，k＞0，分別利用?x∈R，kx²-kx-1＜0是真命題，求出k的范圍．
解答：當(dāng)k=o時(shí)，對(duì)?x∈R，kx²-kx-1＜0，-1＜0即是真命題，成立．
當(dāng)k＜0時(shí)，對(duì)?x∈R，kx²-kx-1＜0是真命題，必有△=（-k）²+4k＜0，
解得，-4＜k＜0，
當(dāng)k＞0時(shí)，對(duì)?x∈R，kx²-kx-1＜0是真命題，顯然不成立．
綜上，-4＜k≤0．
故答案為：-4＜k≤0
點(diǎn)評(píng)：本題考查不等式的解法，恒成立問(wèn)題，考查轉(zhuǎn)化思想，分類討論．