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第206期【试题研修】2026年河北中考数学第15题

当前时间： 2026-07-09 08:50:32 分类：办公文件 评论(0)
第206期【试题研修】2026年河北中考数学第15题

河

北

中

考

2026年

原题呈现

答案解析

01

考点分析

1. 核心知识点：一元二次方程根的定义、根与系数的关系、一元二次方程根的判别式。

2. 关键条件转化：一根是另一根的平方构造方程。
3. 隐含考点：题目明确“有两个实数根”，需要验证判别式，保证解符合题意。

 命题意图

1. 综合考查根与系数的关系与根的倍数、平方类数量关系，是中考代数高频题型。
2. 设置双重约束：①两根满足平方关系；②两根之和为定值，避免学生只列乘积式而忽略和的条件。
3. 增设检验环节，倒逼学生养成解后验证的习惯.
 素养导向
1. 数学运算：熟练运用根与系数的关系建立方程，准确求解一元二次方程。
2. 逻辑推理：根据根的数量关系合理设元，层层推导，严谨取舍根。
3. 严谨求实：利用判别式检验根的有效性，形成完整解题闭环。
典型错因
1. 只利用两根之积列式，忽略“两根之和”这一条件，缺少方程无法求解。
2. 设元后得到高次方程，不会降次化简，计算混乱。
3. 符号出错，混淆两根之和的负号，这是一元二次方程最常见失误。

02

同题异构

1. 变式1：已知一根是另一根的2倍，利用韦达定理求参数m。

2. 变式2：方程两根互为倒数，求字母参数。
3. 变式3：去掉实数根条件，增加多解讨论，训练分类思想。

教学启示

1. 专题梳理根与系数的关系常见题型：倍根、平方根、倒数根、正负根，形成固定解题套路。
2. 反复强调解题流程：设根→利用两根之和列方程→求出根→代入求参数→判别式检验。
3.夯实符号训练，对比练习两根和与两根积的公式，减少符号类低级错误。
4. 把“检验判别式”定为硬性步骤，杜绝只算不验。
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  1. CONNECT:[ UseTime:0.000739s ] mysql:host=127.0.0.1;port=3306;dbname=wenku;charset=utf8mb4
  2. SHOW FULL COLUMNS FROM `fenlei` [ RunTime:0.000806s ]
  3. SELECT * FROM `fenlei` WHERE `fid` = 0 [ RunTime:0.000326s ]
  4. SELECT * FROM `fenlei` WHERE `fid` = 63 [ RunTime:0.000236s ]
  5. SHOW FULL COLUMNS FROM `set` [ RunTime:0.000475s ]
  6. SELECT * FROM `set` [ RunTime:0.000201s ]
  7. SHOW FULL COLUMNS FROM `article` [ RunTime:0.000551s ]
  8. SELECT * FROM `article` WHERE `id` = 845210 LIMIT 1 [ RunTime:0.007886s ]
  9. UPDATE `article` SET `lasttime` = 1783559487 WHERE `id` = 845210 [ RunTime:0.008122s ]
  10. SELECT * FROM `fenlei` WHERE `id` = 64 LIMIT 1 [ RunTime:0.002284s ]
  11. SELECT * FROM `article` WHERE `id` < 845210 ORDER BY `id` DESC LIMIT 1 [ RunTime:0.000551s ]
  12. SELECT * FROM `article` WHERE `id` > 845210 ORDER BY `id` ASC LIMIT 1 [ RunTime:0.000449s ]
  13. SELECT * FROM `article` WHERE `id` < 845210 ORDER BY `id` DESC LIMIT 10 [ RunTime:0.000914s ]
  14. SELECT * FROM `article` WHERE `id` < 845210 ORDER BY `id` DESC LIMIT 10,10 [ RunTime:0.000891s ]
  15. SELECT * FROM `article` WHERE `id` < 845210 ORDER BY `id` DESC LIMIT 20,10 [ RunTime:0.008474s ]
0.122520s