含参数的一元二次不等式专题.pdf

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1、周潭中学-周根虎经典案例分析一二次项系数为常数例 1、解关于 x的不等式：.0)2(2axax解：0)2(2axax)(3243240422aaaa或，此时两根为242)2(21aaax，242)2(22aaax.（1）当324a时，0，)(解集为(248)2(,2aaa)(,248)2(2aaa)；（2）当324a时，0，)(解集为(13,)(,13)；（3）当324324a时，0，)(解集为R；（4）当324a时，0，)(解集为(13,)(,13)；（5）当324a时，0，)(解集为(248)2(,2aaa)(,248)2(2aaa).二二次项系数含参数例 2、解关于 x的不等式：.01)

2、1(2xaax解：若0a，原不等式.101xx若0a，原不等式axxax10)1)(1(或.1x若0a，原不等式.0)1)(1(xax)(文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U

3、1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8

4、F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10

5、Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L

6、7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7

7、A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U

8、10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2其解的情况应由a1与 1 的大小关系决定，故（1）当1a时，式)(的解集为；（2）当1a时，式)(11xa；（3）当10a时，

9、式)(ax11.综上所述，当0a时，解集为 11xaxx或；当0a时，解集为 1xx；当10a时，解集为 axx11；当1a时，解集为；当1a时，解集为 11xax.例 3、解关于 x的不等式：.012axax解：.012axax)(（1）0a时，.01)(Rx（2）0a时，则0042aaa或4a，此时两根为aaaax2421，aaaax2422.当0a时，0，)(xaaaa242aaaa242；当04a时，0，Rx)(；当4a时，0，21)(xRx且；当4a时，0，)(或aaaax242aaaax242.综上，可知当0a时，解集为(aaaa242,aaaa242)；当04a时，解集为R；当4

10、a时，解集为(21,)(,21);当4a时，解集为(aaaa24,2)(,242aaaa).文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5

11、U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6

12、T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D

13、9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:C

14、L5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 H

15、Q6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE

16、4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2三、按方程02cbxax的根21,xx的大小来分类，即212121,xxxxxx；例 4、解不等式)0(01)1(2axaax分析：此不等式可以分解为：0)1(axax，故

17、对应的方程必有两解。本题只需讨论两根的大小即可。解：原不等式可化为：0)1(axax，令aa1，可得：1a当1a或10a时，aa1，故原不等式的解集为axax1|；当1a或1a时，aa1,可得其解集为；当01a或1a时,aa1,解集为axax1|。例 5、解不等式06522aaxx，0a解 原不等式可化为：0)3(2axax，对应方程0)3(2axax的两根为axax3,221，当a0 时，解 集 为axaxx23|或；当0a时，解 集 为|23x xaxa或相关练习训练1、解不等式Rmxxm0141222、解不等式042axx3、解关于x的不等式：033)1(22axxa文档编码:CL5U1

18、0Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7

19、L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q

20、7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5

21、U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6

22、T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D

23、9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2文档编码:CL5U10Y3X3F1 HQ6T7L7U1J7 ZE4D9Q7A8F2