1 . 阅读下题的材料:
已知:
是一元二次方程
的根,求
的值.
小明是这样做的:将
代入
中,得到
;两边同时除以
,得到
;解得
.
小芳觉得小明的做法不对,将其改为:将
代入
中,得到
;移项,得
;解得
,
,
.你认为他们两人的做法正确吗?说明理由.
已知:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d71f015144ffaf1faec94a259b4a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a7c4d0dfb9d54ab20c9292ad40e73e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
小明是这样做的:将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d71f015144ffaf1faec94a259b4a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a7c4d0dfb9d54ab20c9292ad40e73e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acd3a9d53be33f539686be151a9fe804.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4017fa6d1788dffc012660714aa25fbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
小芳觉得小明的做法不对,将其改为:将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d71f015144ffaf1faec94a259b4a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a7c4d0dfb9d54ab20c9292ad40e73e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acd3a9d53be33f539686be151a9fe804.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/154e13a65c8b952148151ff979125caf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a332c554dd20ff0bf0e68c504344a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2f7174773db8f876f5074867c195757.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d64a6593cf2abfcf32a3de5a820762d0.png)
您最近一年使用:0次
名校
2 . 已知
、
是实数,有且只有三个不同的
满足方程
,则
的最小值是_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df63a992490c36c401aa07725c163faf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
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3 . 如果关于
的一元二次方程
有一个根是
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c89c8ae7f2032debe5446546a0cead9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
您最近一年使用:0次
4 . 已知关于x的方程
有一个根是
,那么![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8255d540afdd24f608ab7ec231cff469.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fd6a84d994f86ef1e060e1b1183eeca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8255d540afdd24f608ab7ec231cff469.png)
您最近一年使用:0次
5 . 已知一元二次方程
有一个根是3,那么![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d7679b4cab53ccbe393c292ea3cfcba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
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6 . 已知关于
的一元二次方程
.
(1)如果
是该方程的一个根,求另一个根;
(2)如果方程有两个实数根,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8c13949a6d453c9134ab5864d43fcae.png)
(1)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef00713e73b8357cc7900144f5505bc6.png)
(2)如果方程有两个实数根,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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7 . 若关于
的一元二次方程方程
有一个根为1,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5cd29039f5dbf9ab0cdc72e10d32a33.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcb9ab59137dbd6501d785954414476a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5cd29039f5dbf9ab0cdc72e10d32a33.png)
您最近一年使用:0次
8 . 关于x的一元二次方程
有一个根为0,则m的值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d916c31c7a17b282db87e717f356b7a.png)
A.![]() | B.![]() | C.![]() | D.0 |
您最近一年使用:0次
9 . 已知a是关于x的一元二次方程
的一个根,则
的值等于________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ec4fc05795b158ce3c5025fc5eccee3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a5df06a02dab2dd9d0dbab68cbf0360.png)
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10 . 若
,则关于
的一元二次方程
有一根是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c766352f0be38b719621052de92615bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/807d62d0b5623b3bd3cb285560bf8436.png)
A.1 | B.![]() | C.0 | D.无法判断 |
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