含参数的一元二次不等式的解.pdf
1 含参数的一元二次不等式的解法含参一元二次不等式常用的分类方法有三种：一、按2x项的系数a的符号分类，即0,0,0aaa;例 1 解不等式：0122xaax分析：本题二次项系数含有参数，044222aaa，故只需对二次项系数进行分类讨论。解：044222aaa解得方程0122xaax两根,24221aaaxaaax24222当0a时,解集为aaaxaaaxx242242|22或当0a时，不等式为012x,解集为21|xx当0a时,解集为aaaxaaax242242|22例 2 解不等式00652aaaxax分析因为0a，0，所以我们只要讨论二次项系数的正负。解032)65(2xxaxxa当0a时，解集为32|xxx或；当0a时，解集为32|xx变式：解关于x的不等式1、0)2)(2(axx；2、(1 ax)21.2,2|,1)5(2|,1)4(2,2|,10)3(2|,0)2(22|,0)1(xaxxaxxaaxxxaxxaxaxa或时当时当或时当时当时当【解】由(1ax)21得a2x22ax11.即ax(ax2)0.(1)当a0时，不等式转化为 00，故原不等式无解(2)当 a0，即 x(x2a)0.2a0，不等式的解集为x|2ax02 11|1)5(1)4(11|10)3(1|0)2(1,1|0)1(xaxaaaxxaxxaxaxxa时，当时，当时，当时，当或时，当3、ax2(a1)x10 时，不等式转化为x(ax2)0，不等式的解集为x|0 x2a综上所述：当a0 时，不等式解集为空集；当 a0 时，不等式解集为x|2ax0 时，不等式解集为x|0 x2a文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B53 变式：解关于x的不等式：012xax时，当时，当时，当或时，当41)4(24112411|410)3(1|0)2(2411,2411|0)1(aaaxaaxaxxaaaxaaxxa三、按方程02cbxax的根21,xx的大小来分类，即212121,xxxxxx；例 5 解不等式)0(01)1(2axaax分析：此不等式可以分解为：0)1(axax，故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 6 解不等式06522aaxx，0a分析此不等式0245222aaa，又不等式可分解为0)3(2axax，故只需比较两根a2与a3的大小.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0a时，即23aa，解集为axaxx23|或；当0a时，即23aa，解集为|23x xaxa或变式：1、223()0 xaaxa-+1，或 a0 时，不等式的解为axa2当 0a1 时，不等式的解为a2xa 当 a0，或 a1 时，不等式解为098.0222222aaaaaxx的判别式方程.,221axax得方程的两根为.2,0)3(axaa则若axaa2,0)1(则若.2|,0)3(,0)2(2|,0)1(axaxaaaxaxa时当；时当；时当解集为：综上所述，原不等式的此时解为则原不等式为若,0,0)2(2xa文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B54 课后练习：1、)23(0)3)(2(aaxxax，且（分3;32;2aaa讨论）3,2|3)3(3,2|32)2(32,|2)1(axxxaxaxxaxaxxa或时，当或时，当或时，当2、不等式11xax的解集为 21|xxx，或，求a的值.（21a）3、已知0)1(|,023|22axaxxBxxxA，若AB，求实数a的取值范围.；（2a）若AB，求实数a的取值范围.；（21a）若BA为仅含有一个元素的集合，求a的值.（1a）解：A=x1x2，B=x(x-1)(x-a)0(1)若 A B(图甲)，应有 a2.(2)若 BA(图乙)，必有 1a2.(3)若 AB 为仅含一个元素的集合(图丙)，必有 a1.4、已知031|xxxA，BBAaxaxxB且,0)1(|2，求实数a的取值范围.（31a）5、设全集RU，集合3|12|,01|xxBxaxxA，若RBA，求实数a的取值范围.（12a）6、已知全集RU，034|,082|,06|2222aaxxxCxxxBxxxA，若CBA)(，求实数a的取值范围.（21a）7、若关于x的不等式(2x1)2ax2的解集中的整数恰有3 个，求实数a的取值范围。（1649925a【解析】不等式可化为(4 a)x2 4x 1 0，由于原不等式的解集中的整数恰有3 个，所以0)4(41604aa，解得 0a4，故由得axa2121，又212141a，所以解集中的3 个整数必为1,2,3，所以 3a214，解得925a1649文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5文档编码:CG2X6F9O1X6 HH9W7H7B6X2 ZB8L7B8I5B5
