Question

-4＜k＜0是函數(shù)y=kx²-kx-1恒為負值的    條件．

Answer 1

【答案】分析：函數(shù)y=kx²-kx-1恒為負值?①k=-k=0，-1＜0滿足，或者②⇒-4＜k＜0，根據(jù)充分、必要條件的定義即可得到答案．
解答：解：要使函數(shù)y=kx²-kx-1恒為負值，則k須滿足：
①k=-k=0，-1＜0，解得k=0；
②即解得-4＜k＜0；
∴-4＜k＜0⇒函數(shù)y=kx²-kx-1恒為負值，即-4＜k＜0是函數(shù)y=kx²-kx-1恒為負值的充分條件成立；
但是，函數(shù)y=kx²-kx-1恒為負值卻不能推出-4＜k＜0，即-4＜k＜0不是函數(shù)y=kx²-kx-1恒為負值的必要條件；
故答案為：充分不必要．
點評：本題考查二次函數(shù)的性質(zhì)與必要條件、充分條件與充要條件的判斷，難點在于“函數(shù)y=kx²-kx-1恒為負值”的充要條件的探究，易錯點在于對“必要條件、充分條件與充要條件”概念的理解與應用，屬于中檔題．