解题方法
1 . 已知函数
,
的零点分别是
与
.
(1)若
,解不等式
;
(2)已知
,
①证明:
;
②若
,
满足
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3023e7cb9c12cd7789dd5babcbc81bfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/460fb23be742df604c9e3acbadb975d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c97b49ac1c01655ddceb48cc71585f62.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d755a0a76e2102eb6e29db34df0903dd.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/123371927e0a2f94563eb7321039dfbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ceddc345bfa05b7c0c61ec02470188a.png)
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解题方法
2 . 我们知道,一个一元一次方程最多有一个根,一个一元二次方程最多有两个根,这些都是代数基本定理的简单表示,代数基本定理可以表述为:一元n次多项式方程最多有
个不同的根.由代数基本定理可以得到如下推论:若一个一元
次方程有不少于
个不同的根,则必有各项的系数均为0.已知函数
,函数
的图象上有四个不同的点A、B、C、D.利用代数基本定理及其推理回答下列问题:
(1)解关于x的方程
;
(2)是否存在实数
,使得关于
的方程
有三个以上不同的解,若存在,求出
的值,若不存在,请说明理由;
(3)若
按逆时针方向顺次构成菱形,设
,求代数式![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa8a18548e00a131abe2eca8c4c815c2.png)
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0876215b2fd463d151523cd3c6b447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7bc57a9ac3f82c3b8af4fe78e5c861b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)解关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b070bfc31cef4c001541af54d3c36cd3.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb2158cfb945452be603a745510df299.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0877194ab8760f54c35527177b03ff93.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0b032796d46540441098204aa82c12a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa8a18548e00a131abe2eca8c4c815c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c004d926a934cced9bc523a8ecde1df1.png)
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3 . 已知函数
在
内恰有两个不同的零点
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97dad16e4910ec15add074c4077b0e86.png)
__________ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d052f5c44e99d0dbe66f438388c517c2.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4dbd5e98eface20d7122a32d21a477f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b23efa380a58dc9663ba06dc249ce721.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97dad16e4910ec15add074c4077b0e86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d052f5c44e99d0dbe66f438388c517c2.png)
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2024-06-03更新
|
358次组卷
|
2卷引用:辽宁省本溪市县级重点高中协作体2023-2024学年高一下学期期中考试数学试卷
4 . 若关于
的不等式
的解集为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cad7dfbef17526340703455faf026a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe5239e374894f95da60c5cb35a2a718.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
5 . 若函数
的零点为
,函数
的零点为
,则下列结论正确的是__________ .
①
; ②
; ③
; ④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c610be51805afc89b890371f444db34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a8e2324eba1bb259a4e43cc66900c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e8d686883e028695be53ba0922bd91f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/358457d692e279ee036e7753be4ebb23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8f1c8aff3680364230aed57c5b9f44a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee10bfaa227fd231847fd3590fe5e773.png)
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6 . 已知函数
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc1b193aa193153eb402df8560778e6.png)
A.函数![]() |
B.若![]() ![]() |
C.若![]() ![]() |
D.当![]() ![]() ![]() |
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解题方法
7 . 已知函数
.若
,则
的零点为________ ;若函数
有两个零点
,
,则
的最小值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59ff5494511e8589c702bba82b297cb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a882037b9ce104ecc496e0f31a139361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd888afdcfdb3e91a157d50f65e915e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/920afbbef7b1845de8b24534f6f151f5.png)
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8 . 已知
是定义域为
的奇函数,函数
,且当
时恒成立,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c19b5e7ec97fb0dc579c3f0c47f2727.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/967d2a64967055bf7847d26f5eb7bb08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f66193ff4404822ce1410b60d251569.png)
A.![]() | B.不等式![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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解题方法
9 . 已知函数
,
,若
有两个零点
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f98fc3ebd8871c2c959090a8d22e951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e10dce73bdc1d522ae7cb34805ed3d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2024-03-29更新
|
820次组卷
|
3卷引用:湖北省(圆创)高中名校联盟2024届高三下学期3月月考数学试题
10 . 已知函数
的零点从小到大分别为
.若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/841e18965314d5feeaf175120385d29f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb978c7b420799301ed8cdcfda26a127.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e23a44c29788c2ffef523252d5c8aaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9448bf1d6136b3a108e7ea60506ad39.png)
A.![]() | B.![]() | C.![]() | D.3 |
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