2024八年级下·上海·专题练习
1 . 方程
的解是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/add31370d649083a9820dff3af8ecd04.png)
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2 . 设关于
的方程
(
是常数)的三个解是
三条边的边长,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751a4e4491bbe6612bc8644bbbde52b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
3 . 如图,四边形
,
,
,
,
,点
在线段
上,当
为等边三角形时,线段
的长为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd0ca91fd654229e128e415b983e433f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a6747120be6416f017e20c7d841ed2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8feb9fdc5582ad3e9853890ac2738d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebf581fd67327eaed22bd2c613aee299.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbc2757873908ca1fd07e1fe7ae167e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a6c6e7c025362c46a64a8956761f08e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
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4 . 解方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c824c2691c002ca68f3f19b80c433c56.png)
您最近一年使用:0次
5 . 已知关于
的方程
有一个实数根是
,那么
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8642e00c340026414ea8c3944cd80c90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.2 | B.3 | C.2或3 | D.一切实数. |
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6 . 方程
的根是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44469720e955dd50bf14ac4aac9eae10.png)
您最近一年使用:0次
名校
7 . 方程
的根是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f606c9094ae64f4233ddd48ac861cbf5.png)
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8 . 方程
的解有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/181a39dc4c7b34162f11be6a24429ae9.png)
A.![]() | B.0 | C.4 | D.16 |
您最近一年使用:0次
23-24九年级上·湖南·阶段练习
9 . 【引入命题】设
是关于字母
的一个整式,若
是方程
的一个根,则整式
必有一个因式
,即
.其中
仍然是关于字母
的一个整式.
(1)若
,则
的一个根是___________;
【回归课本】设一元二次方程
有两个根
,
,则方程可化为:
,即
,与原方程比较系数,可得到一元二次方程根与系数的关系:
,
.
(2)利用上式结论解题:已知关于
的一元二次方程
有两个不相等的实数根,且
,求实数
的值;
【探究引申】设一元三次方程
有三个根
,
,
,则原方程可化为:
,试着展开上式,然后比较系数,可以得到根与系数的关系:
,
,
.
(3)利用上式结论解题:已知方程
有三个根
,
,
,求
的值;
【拓展提高】
(4)利用以上规律探究:若方程
有
个根
,
,…,
,则
____________,
_____________.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7303a4f91bf736f860d2e6a818a393d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab6e6b9250ebb2b94f73f5fc83b72ea0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7303a4f91bf736f860d2e6a818a393d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3a5613e7b4d4f9c1c5b2cc6360267d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebd0f5b32cc913aa564b3759e3cc6968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ca1c244f174b75249fa318b5e36dc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ea4c0193fd81496df0374c1b901855.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab6e6b9250ebb2b94f73f5fc83b72ea0.png)
【回归课本】设一元二次方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13fa32c1e926f40a0722d106563777ef.png)
![](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/00c6318d68e82894d4b12da3a2bc47ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ef9548411a12684e1dbb763fa45ed06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f05dd02b6f561dcf94bab8a3160108d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/897630dd340ec6c6b20cdd754d0a12c9.png)
(2)利用上式结论解题:已知关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adbaa19ff682c6e8cede4405495fddbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71e814cb5f44aecd916fb2fc4891ca8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
【探究引申】设一元三次方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48ad9d68d15b5d5121fcf99ebddaa986.png)
![](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/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ff0277c38f2cb116e87d5d8d124831.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c42879b831382d3d84c43a70a3ed78f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6794011ce5d1e2ee33c1f316242504b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0590305964aa6cf9f7fd1e60d477e309.png)
(3)利用上式结论解题:已知方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7851e92b7092cd42c2c99e8d5a4c5c28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19b04136aa3cc67329234da47b901038.png)
【拓展提高】
(4)利用以上规律探究:若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94719dbb176c613280820c23b9dba41e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](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/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fa75c6217e24a7ac76ff0af8b6f91ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c72fd81f261f6e7325fc57697480101.png)
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10 . 解方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b12f044e6f25745d52cdafd3a04a76a.png)
您最近一年使用:0次