1 . 下列关于一元二次方程x2+bx+c=0的四个命题
①当c=0,b≠0时,这个方程一定有两个不相等的实数根;
②当c≠0时,若p是方程x2+bx+c=0的一个根,则
是方程cx2+bx+1=0的一个根;
③若c<0,则一定存在两个实数m<n,使得m2+mb+c<0<n2+nb+c;
④若p,q是方程的两个实数根,则p﹣q=
,
其中是假命题的序号是( )
①当c=0,b≠0时,这个方程一定有两个不相等的实数根;
②当c≠0时,若p是方程x2+bx+c=0的一个根,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/966bc353f87f70031caea835d1335723.png)
③若c<0,则一定存在两个实数m<n,使得m2+mb+c<0<n2+nb+c;
④若p,q是方程的两个实数根,则p﹣q=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d7b7cc118d40ffd019d7411ec4cfbc.png)
其中是假命题的序号是( )
A.① | B.② | C.③ | D.④ |
您最近一年使用:0次
2 . 发现思考:已知等腰三角形
的两边分别是方程
的两个根,求等腰三角形
三条边的长各是多少?下边是涵涵同学的作业,老师说他的做法有错误,请你找出错误之处并说明错误原因.
涵涵的作业:
解:
.
,
,
.
,
①
.
②
,
.
③
所以,当腰为5,底为2时,等腰三角形的三条边为5,5,2.
④
当腰为2,底为5时,等腰三角形的三条边为2,2,5.
⑤
(1)涵涵的作业错误的步骤是_____(填序号),错误的原因是____.
(2)探究应用:
请解答以下问题:
已知等腰三角形
的一腰和底边的长是关于
的方程
的两个实数根.
①
时,求
的周长;
②当
为等边三角形时,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1547524e9dcbc789b785c4e2970fcdba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
涵涵的作业:
解:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1547524e9dcbc789b785c4e2970fcdba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5032113438f38f1b2d7b270e803d1837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6d39e8c6fc9149d6290c493a65bdc53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06dd9c262b8296810f49245d30fbf686.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccc99dfaa5d6d4bd4159576757842a31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69e69a44ed9e0d9028267aed4fb430a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccc99dfaa5d6d4bd4159576757842a31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1801db0d79a8a923b52522c2d320f4ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/204e5160ff110a19878e4fae639319e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccc99dfaa5d6d4bd4159576757842a31.png)
所以,当腰为5,底为2时,等腰三角形的三条边为5,5,2.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccc99dfaa5d6d4bd4159576757842a31.png)
当腰为2,底为5时,等腰三角形的三条边为2,2,5.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccc99dfaa5d6d4bd4159576757842a31.png)
(1)涵涵的作业错误的步骤是_____(填序号),错误的原因是____.
(2)探究应用:
请解答以下问题:
已知等腰三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37db8f1255a6ee61a7a024eee8b27531.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94f16d5ed858699bfea5039a7bf8ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2021九年级上·全国·专题练习
3 . 如果关于
的一元二次方程
有两个相等的实根,那么对于以
,
,
为边的三角形,下面的判断不正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9532a934b6aef4b6d59e358e79b5323.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
A.以![]() | B.以![]() |
C.以![]() | D.以![]() |
您最近一年使用:0次
4 . 若抛物线
与x轴有交点,求a的取值范围.
晓莉的解题过程如下:
∵抛物线
与x轴有交点,
∴
,即
,
∴
.
请问晓莉的解题过程是否正确?如果不正确,请改正.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5625cf9bb5e46e3a700a9a4c7d9fe783.png)
晓莉的解题过程如下:
∵抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5625cf9bb5e46e3a700a9a4c7d9fe783.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62a705693dc3a46035b0bb1c81d0158b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d22717cea317699d061edc58a284558.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daadfc8469fb7fda0a84ffc387abe08c.png)
请问晓莉的解题过程是否正确?如果不正确,请改正.
您最近一年使用:0次
5 . 抛物线
(a,b,c是常数,
)经过
,
,
三点,且
.在下列四个结论中:①
;②
;③当
时,若点
在该抛物线上,则
;④若关于x的一元二次方程
有两个相等的实数根,则
;其正确结论的序号是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90385c676848de67293e3ed6bc000fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f75807858b7804a1ad2039c41f323a18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c832f2474efe89961ef41e884da7660c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b67c623950b5795d5fb4daeb8102a8df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae3a88c614758672f5d2f2149236476.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12e7ef804eeb23618fbf91ead47587f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a3baf3050d0514f2fac97fda89653f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caff39fdb463050709ad1478b8b485dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6057df53aac56374ddf8146623f64678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/106075af36f5fbb556ef0835fa3cd75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/660f3532dad8eaae789d09552d1345c9.png)
A.②③④ | B.①②④ | C.①②③ | D.①③④ |
您最近一年使用:0次
6 . 在平面直角坐标系
中,点P的坐标为
,称关于x的方程
为点P的对应方程.如图,点
,点
,点
.
给出下面三个结论:
①点A的对应方程有两个相等的实数根;
②在图示网格中,若点
(
均为整数)的对应方程有两个相等的实数根,则满足条件的点P有3个;
③线段
上任意点的对应方程都没有实数根.
上述结论中,所有正确结论的序号是____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7204f43679af6935e494c59d40c6ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f43e49552a5099a8b2a442247c65a243.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0929421a6188c3122442866b0b85a5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d3bfa155ad67018da4d65815c5e5b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21ee34df0156dc705b1b2444471ff373.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/10/d090d08e-7d82-4e12-9615-e5e11d99eaff.jpg?resizew=180)
给出下面三个结论:
①点A的对应方程有两个相等的实数根;
②在图示网格中,若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82aaa597a5aa6176863eda3fdf83e181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
③线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
上述结论中,所有正确结论的序号是
您最近一年使用:0次
2023-11-01更新
|
193次组卷
|
2卷引用:北京市海淀区2023-2024学年九年级上学期期中数学试题
7 . 若关于
的一元二次方程
有两个不相等的实数根
,
,且
.
(1)下列说法正确的有_____ .(将正确选项的序号填在横线上)
①若
,则
;
②
;
③若
,则
;
④若
,则
.
(2)某数学兴趣小组为了增加此题的趣味性,将题目改成:若关于
的方程
有两个不相等的实数根
,
,且
,其中
,
,
均为整数,则
的最小值为 _____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92b800b7d6a688abf8a3018c133cec9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b916df8bdd03ba4a31c0b8470d13436.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb5ffa21fddc7c55d35f13435792b2d4.png)
(1)下列说法正确的有
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2fe3251e054fe97089806ba7033f802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f75807858b7804a1ad2039c41f323a18.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34eaf0aa0ab112622e9ed24f2ca85db1.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4d57bdb85ad21a427ebc3126fab41ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c56b1ee18c6809b339d980671b4d09a.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb0c4d00b3592435032883c42683da86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc1adacd10539c74b82fc1e6e88ea6f6.png)
(2)某数学兴趣小组为了增加此题的趣味性,将题目改成:若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9c0dce1f975d1203a1bff7580a892d.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/e097f28b6443848c98413364953c37ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-10-24更新
|
239次组卷
|
2卷引用:2021年湖北省武汉市洪山区华中师大一附中自主招生数学试题
8 . 二次函数
(
,
,
是常数,
)的图象与
轴交于点
,
.下列说法中:①一元二次方程
的根为
,
;②
;③对于
的每一个确定的值,若一元二次方程
(
为常数,
)的根为整数,则
的值只有两个;④若点
,
在该二次函数的图象上,则
.正确结论的序号是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90385c676848de67293e3ed6bc000fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0929421a6188c3122442866b0b85a5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ef03f452410ab19c6246567c427178.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13fa32c1e926f40a0722d106563777ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a60302649eb940748da818199e55da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acb35c769007b54a0204e85a0e5223bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/375386102cba5bfd93bdf340216eb22d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a2dad4e1968586bd34415bb3a67e9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7be8524456ba4e9abb973da323c0c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbc298508238501416c1ebd104e569f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd343e3c3d252bc27f97b76dfe9f177d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f99df1a7b58018125b99578b779342.png)
您最近一年使用:0次
9 . 在学习一元二次方程的根与系数关系一课时老师出示了这样一个题目:已知关于x的方程
的两实数根为
,
,若
,求m的值.
波波同学的解答过程如框:
波波的解法是否正确?若正确请在框内打“√”;若错误请在框内打“×”,并写出你的解答过程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21202e8821c7c0870f32a3b4cdecc275.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/e681544811d9ccc18a5039ccddbe1583.png)
波波同学的解答过程如框:
解: 由题意可知: ![]() ∵ ![]() ∴ ![]() 解得: ![]() ![]() |
您最近一年使用:0次
10 . 下列命题正确的是(填序号)_____ .
①
的立方根是2;②一组数据的方差越大,这组数据波动性越大;③方程x2+2x-3=0有两个不相等的实数根;④平分弦的直径垂直于弦;⑤等边三角形是中心对称图形.
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2b57621e687a87d1bbf76532dad2ecc.png)
您最近一年使用:0次