名校
1 . 设函数
的导函数为
的导函数为
的导函数为
.若
,且
,则
为曲线
的拐点.
(1)判断曲线
是否有拐点,并说明理由;
(2)已知函数
,若
为曲线
的一个拐点,求
的单调区间与极值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a00a7220fe1f1699aa32ea0c70a303.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2183b5237f02670ccbe463aaaca37977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca0b72923071c1010a36f17cb3d1168b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca411f2905fd482bd14cb0092e5a6279.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ea9154699908e7a530d9e04830c9315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)判断曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c683786f6c924632d9ca47ea243700e7.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/341534f0072c55c40cc00ed25097c2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9bfaad7a770a2bb3930de1ed7444d90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
昨日更新
|
309次组卷
|
4卷引用:河南省部分重点高中2023-2024学年高三下学期5月联考数学试卷 (新高考)
河南省部分重点高中2023-2024学年高三下学期5月联考数学试卷 (新高考)(已下线)辽宁省沈阳市第二中学2024届高三下学期三模数学试题2024届青海省海南藏族自治州高考二模数学(理科)试卷内蒙古自治区锡林郭勒盟2024届高三下学期5月模拟考试理科数学试题
解题方法
2 . “费马点”是由十七世纪法国数学家费马提出并征解的一个问题,该问题是:“在一个三角形内求作一点,使其与此三角形的三个顶点的距离之和最小”.如图1,三个内角都小于
的
内部有一点
,连接
,求
的最小值.我们称三角形内到三角形三个顶点距离之和最小的点为费马点.要解决这个问题,首先应想办法将这三条端点重合于一点的线段分离,然后再将它们连接成一条折线,并让折线的两个端点为定点,这样依据“两点之间,线段最短”,就可求出这三条线段和的最小值.某数学研究小组先后尝试了翻折、旋转、平移的方法,发现通过旋转可以解决这个问题,具体的做法如图2,将
绕点
顺时针旋转
,得到
,连接
,则
的长即为所求,此时与三个顶点连线恰好三等分费马点
的周角.同时小组成员研究教材发现:已知对任意平面向量
,把
绕其起点沿逆时针方向旋转
角得到向量
.
,把点
绕点
沿顺时针方向旋转
后得到点
,求点
的坐标;
(2)在
中,
,借助研究成果,直接写出
的最小值;
(3)已知点
,求
的费马点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/231b861d6d1f1d0b9f52b041cb40eb62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19bb1063e139610045f3bca5ca0b2766.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7ed53a398b1d6b7b4abbb43a9abcf1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9524e3810e06dc781285f1289e75d653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f850c705372b8a85489505da53239fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5643311f49a8c6f64b2a2788f79458e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f478a74bccc9b8d7745b08c5484f238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb5d89b04570ceda2c29e11cb27a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89756ef947f1add6a68efa8998430dc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7de03fc9682ff77d327a5681010ab3b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b11bf8ee11289d13cf5dd0ea9505e699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7ed53a398b1d6b7b4abbb43a9abcf1f.png)
(3)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a65f35281b21fdfaf7c437fbd321eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
解题方法
3 . 某学校开展社会实践进社区活动,高二某班有
六名男生和
四名女生报名参加活动,从中随机一次性抽取5人参加
社区活动,其余5人参加
社区活动.
(1)求参加
社区活动的同学中包含
且不包含
的概率;
(2)用
表示参加
社区活动的女生人数,求
的分布列和数学期望.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b391f13d12d569854368bf34d4201ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfdacf462cf48a7101c4773a8c619eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)求参加
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/011ae6cb0cf49f6d3d19b485dc1cfc22.png)
(2)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
您最近一年使用:0次
名校
解题方法
4 . 如图,已知
分别是三棱锥
棱
上的点.
为平行四边形,证明:
面
;
(2)若
分别是
的中点,且
,直线
和直线
所成角为
,求直线
和直线
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d45053e5879b431923e0d53b57091f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a94d59dee2d5a8f0425b64b2083825.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/068eeefc0c19329cc04ff28ba51ac090.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ac79e422ba4876949f0514c44539b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce3da36477d98f47fff39520e496617.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ac79e422ba4876949f0514c44539b1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b1e6d86c5142ba1576cc277dbf32994.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1655c164ebe93332ef4d9fed6bdeb04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7288db347b6e10d3d679d4030c857a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4fce8e923062b9779553d6f282895b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4fce8e923062b9779553d6f282895b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce2790947716b1cfa9c5e7a65db4093.png)
您最近一年使用:0次
5 . 利普希兹条件是数学中一个关于函数光滑性的重要概念,设
定义在
上的函数,若对于
中任意两点
,都有
,则称
是“
-利普希兹条件函数”.
(1)判断函数
,
在
上是否为“1-利普希兹条件函数”;
(2)若函数
是“
-利普希兹条件函数”,求
的最小值;
(3)设
,若存在
,使
是“2024-利普希兹条件函数”,且关于
的方程
在
上有两个不相等实根,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9f58d4591d668b4bc32fae4faab8298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2712b1acecc1d933cca91078b76ffea2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ab466aedd6e176088d8dee7bc3e3aaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44edb8cc6555fc6ec8d0bfd7d5b33f0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1044dcf4fba551e1b7fbfeb895ea08c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c51159984b2cb00f30b3986315019623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e711f9ca607fd1b077e742d1cc156bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f172b078edc129d4ad341fc2bfb13d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92538987cf225663a769b58a933ac6af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
解题方法
6 . 已知圆
,直线
,直线
和圆交于A,B两点,过A,B分别做直线
的垂线,垂足为C,D.
(1)求实数b的取值范围;
(2)若
,求四边形ABDC的面积取最大值时,对应实数
的值;
(3)若直线AD和直线BC交于点
,问是否存在实数
,使得点
在一条平行于
轴的直线上?若存在,求出实数
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79382ba44ba669b5d43fdd5427adf16c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13b673b7961af5c4b51e67d6ffe00912.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aa941aa5d428f5d78ec3f281464f826.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
(1)求实数b的取值范围;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdbf6506e9de40da0f3c51b81b35a901.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(3)若直线AD和直线BC交于点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
7 . 已知
,动点
满足
,动点
的轨迹为曲线
交
于另外一点
交
于另外一点
.
(1)求曲线
的标准方程;
(2)已知
是定值,求该定值;
(3)求
面积的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/107a80eeecf2efcb25cb008945c1c241.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cced7a3d18b398c1da1218d74a96542.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ac4aa6db80d4edfd287abc4580e68b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09757d013574cf058d5bb944fdf034a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c72be8e3e113103ca7de54ac39c2313.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09757d013574cf058d5bb944fdf034a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09757d013574cf058d5bb944fdf034a.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da79ae7251aa6d5822b5396a632b01c7.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c28abb154f41e1ca9816c9c9c2433ca.png)
您最近一年使用:0次
7日内更新
|
646次组卷
|
3卷引用:浙江省宁波市镇海中学2024届高三下学期适应性测试数学试卷
解题方法
8 . 如图所示,已知点
,
轴于点
,点
为线段
上的动点(
不与端点
重合),
轴于点
,
于点
,
与
相交于点
,记动点
的轨迹为
.
的方程;
(2)点
是
上不同的两点,
关于
轴对称的点为
,记直线
与
轴的交点为
,直线
与
轴的交点为
.当
为等边三角形,且
时,求点
到直线
的距离的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4fe7df5efe498440449d4c2b340df0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b45db8dd8768994af51206565379fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ffc62c28c53286cd17e9eb997af7221.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcec4050ad922c18239c38effcc45403.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc0e7a1541a8db0c059fd6cd0c4c3620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83042953e7f15e984b2da2ee9ca678d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b3265b7f882e7430dcfc27304bef3c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28b1ba4307cfde9b424d468bfcdf6c5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e91df8b5d2d51900151398baf13a15d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7463328ad1cffdd1a841aba1b2b3f7b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07d824821175f4e0e7803cadf921e48e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9554c404e670a784d9a7e4df26ecd001.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
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9 . 已知数列
,
,函数
,其中
,
均为实数.
(1)若
,
,
,
,
,
(ⅰ)求数列
的通项公式;
(ⅱ)设数列
的前
项和为
,求证:
.
(2)若
为奇函数,
,
,
且
,问:当
时,是否存在整数
,使得
成立.若存在,求出
的最大值;若不存在,请说明理由.(附:
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2b44ac9ffc5dd71901d5cae704f059.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09881de0dc186bbcd1e60eb00159ee97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88f2599ca8b6b683e57a82699c8b1ebb.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b970d657304931a9d5cecdb044968f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a783088120d67cc98936081e80fb7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32003b56a60c9977c5d5d667c4136f62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385275d29d8c8a7841eaeaa3dfab2cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51b14938503c29201f32d30deda61db3.png)
(ⅰ)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
(ⅱ)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411bfe81694849b77de8b87f2651975a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43af3d8ebe0e5f0a905d42d29afe6f6f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66e442aaf3fda101960c18cc41de1614.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d39c60d4618060bbdc332282f0a0dd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f7cc67b3e263a2562be3c4c80dd5a5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bfb7ad7e6f4bbe0ec8dc3bec7d49025.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570c49bcd783ed65a16b7bc565347094.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0e474d29ab7f3a4e404f593e90ae8b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c1868215cf7dbeb9dd228d2cede3e9.png)
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名校
10 . 代数基本定理:任何一个
次复系数多项式方程
至少有一个复根.由此可得如下推论:
推论一:任何一元
次复系数多项式
在复数集中可以分解为
个一次因式的乘积;
推论二:一元
次多项式方程有
个复数根,最多有
个不同的根.即一元一次方程最多有1个实根,一元二次方程最多有2个实根等.
推论三:若一个
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
.请利用代数基本定理及其推论解决以下问题:
(1)求
的复根;
(2)若
,使得关于
的方程
至少有四个不同的实根,求
的值;
(3)若
的图像上有四个不同的点
,以此为顶点构成菱形
,设
,
,求代数式
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab009a153dfcc13ba9eb4916c76f8ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b7bff9b2431134f7683a9cc4e68acd.png)
推论一:任何一元
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab009a153dfcc13ba9eb4916c76f8ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
推论二:一元
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
推论三:若一个
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0876215b2fd463d151523cd3c6b447.png)
已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b14c686bfce270ec65d068555d1866ff.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dadabea3f5008d97a32382752e62bdd8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec4e65c4c043edef8084b292675395c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcecb855c13987b207aec2db73c9ec5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c82a10b4f0c9323d726804c89dd9548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc04eee630e386f7be4ac709ff4e16c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df74fc4cedb204eb6dcce64b706e99c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed0c942fae0e9dd2d219ad8269511898.png)
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