1Â¥£º
µÂ¶ûËþ´óÓÚµÈÓÚ0µÄ»°º¯ÊýÖµÖÁÉÙÓÐÒ»¸öÊÇ0
Ò»¸ö¶þ´Îº¯ÊýµÄֵСÓÚ0£¬ËµÃ÷ËüµÄdeltaÒ»¶¨Ð¡ÓÚ0Âï
2Â¥£º«hµ¿
Ò»¸ö¶þ´Îº¯ÊýµÄÖµÖ¸µÄÊǶþ´Îº¯ÊýÉϵãµÄ×Ý×ø±êµÄÖµ£¬¶øÄã˵µÄdeltaÒ²¾ÍÊÇ¡÷=b^2-2ac
¡÷<0±íʾ¶þ´Îº¯ÊýÓëxÖáûÓн»µã
¡÷=0£º¶þ´Îº¯ÊýÓëxÖáÖ»ÓÐÒ»¸ö½»µã£¬¾ÍÊǶ¥µãÔÚxÖáÉÏ¡÷>0£º¶þ´Îº¯ÊýÓëxÖáÓÐÁ½¸ö½»µã
ËùÒÔ¶þ´Îº¯ÊýµÄÖµÓëdeltaµÄֵûÓйØϵ
3Â¥£ºÄäÃûÓû§
½â£ºÒ»¸ö¶þ´Îº¯ÊýµÄֵСÓÚ0£¬¡÷²»Ò»¶¨Ð¡ÓÚ0£¬
µ±¶þ´ÎÏîϵÊý´óÓÚ0ʱ£¬¶þ´Îº¯ÊýµÄֵСÓÚ0£¬Ôò¡÷>0;
µ±¶þ´ÎÏîϵÊýСÓÚ0ʱ£¬¶þ´Îº¯ÊýµÄֵСÓÚ0£¬Ôò¡÷<0¡£
4Â¥£ºÍÛßÇßÇ
Êǵģ¬²¢ÇÒ¿ÉÒÔÖªµÀÕâ¸öÅ×ÎïÏß¿ª¿Ú·½ÏòÏòÏ£¬µ±È»¶¨ÒåÓòxΪÈÎÒâʵÊý£¬Èç¹ûûÓÐÕâЩÏÞ¶¨Ìõ¼þÊDz»¿ÉÒÔµÄ
5Â¥£ºÄäÃûÓû§
a>0ʱ,¶þ´Îº¯ÊýµÄֵСÓÚ0,delta´óÓÚ0´æÔÚ,,Á½¸ùÖ®¼äº¯ÊýµÄֵСÓÚ0
a<0ʱ,¶þ´Îº¯ÊýµÄֵСÓÚ0,˵Ã÷ËüµÄdeltaÒ»¶¨Ð¡ÓÚ0
6Â¥£ºä²ÒÔ³Ééä
Òª¿´ËüµÄÖµÊDz»ÊǶ¼Ð¡ÓÚ0
ÔõÑùʹ¶þ´Îº¯Êýºã´óÓÚ»òСÓÚÁ㣿µÂ¶ûËþÒªÔõÑù£¿
7Â¥£ºÄäÃûÓû§
µ±a£¾0ʱ£¬yÖ»¿ÉÄÜÓкã´óÓÚ0µÄÇé¿ö£»
µ±a£¼0ʱ£¬yÖ»¿ÉÄÜÓкãСÓÚ0µÄÇé¿ö¡£Á½ÖÖÇé¿ö¶¼ÒªÇó¦ÄºãСÓÚ0
8Â¥£ºÄäÃûÓû§
1.a>0ʱ£¬¿ª¿ÚÏòÉϵ¶ûËþСÓÚÁã
£¬Ôòº¯Êýºã´óÓÚÁãµÂ¶ûËþ´óÓÚÁ㣬Ôòº¯ÊýÁ½¸ùÖ®ÍâµÄº¯ÊýÖµ´óÓÚÁ㣬Á½¸ùÖ®Äڵĺ¯ÊýֵСÓÚÁã¡£2.a<0ʱ£¬¿ª¿ÚÏòϵ¶ûËþСÓÚÁ㣬Ôòº¯ÊýºãСÓÚÁãµÂ¶ûËþ´óÓÚÁ㣬Ôòº¯ÊýÁ½¸ùÖ®ÍâµÄº¯ÊýֵСÓÚÁ㣬Á½¸ùÖ®Äڵĺ¯ÊýÖµ´óÓÚÁã¡£
9Â¥£ºÄäÃûÓû§
»Í¼Ïñ¡£ºóÃæµÄÎÊÌâÊÇ£º´óÓÚ0¡£
·½³ÌÓÐÁ©²»Ò»ÑùµÄ½â µÈÓÚ0,¡£·½³ÌÓÐÁ©Ïàͬ¸ù¡£ СÓÚ0.
·½³ÌÎÞʵ¸ù¡£
¶þ´Îº¯Êý¶¨ÒåÓòΪrºã³ÉÁ¢ÎªÊ²Ã´¡÷¡Ü0
10Â¥£º
¶÷£¬°´ÕÕËûµÄ½âÌâ˼·£¬Ó¦¸ÃÊÇÁîu=(a2-1)x2+(a-1),f(x)=¸ùºÅÏÂu
ÒòΪÓиùºÅµÄ´æÔÚ£¬ËùÒÔÒªÇó¶¨ÒåÓòf(x)µÄʱºòÊÇÒª±£Ö¤±»¿ª·½Êý·Ç¸º£¬¼´u¡Ý0
(×¢ÒâÊÇu¡Ý0,¶ø²»ÊÇu>0£¬ËùÒÔÄãµÄÄǸö¡°ÒªÊ¹uºãΪ·Ç¸º£¬µÃ³öu>0¡±ÊÇ´íµÄ£¬Êǵóöu¡Ý0,
ËùÒÔ¡÷=0ʱÓÐÒ»¸ö½»µã£¬ÄÇʱu=0£¬ÊÇ¿ÉÒÔµÄ)
¶øҪʹu¡Ý0£¬u=(a2-1)x2+(a-1)£¬¼´u±¾ÉíÊÇÒ»¸ö¶þ´Îº¯Êý£¬ÒªÊ¹¶þ´Îº¯ÊýµÄÖµÓòºã·Ç¸º£¬µ±È»
Ê×ÏÈÒªÇó¶þ´Îº¯ÊýͼÐοª¿ÚÏòÉÏ°¡£¬
Õâ¾ÍÒªÇó¶þ´ÎÏîϵÊýa2-1>0(¿ª¿ÚÏòϵĶþ´Îº¯ÊýµÄÖµÓò£¬ÊDz»¿ÉÄÜÓÀÔ¶´óÓÚµÈÓÚ0µÄ°¡£©
Æä´Î£¬ÔÚ¿ª¿ÚÏòÉϵĻù´¡ÉÏÒªÇóÓëxÖá×î¶àÓÐÒ»¸ö½»µã£¬ËùÒÔ¡÷¡Ü0£¬·ñÔòº¯ÊýͼÐεÄijһ¶Î¾Íµôµ½xÖáÏ·½È¥ÁË£¬Ò²ÊDz»¿ÉÄܺãΪ·Ç¸ºµÄ
11Â¥£ºÄäÃûÓû§
¡÷¡Ü0˵Ã÷ͼÏñÓëxÖáÎÞ½»µã£¬ÓÖÒòΪ·½³Ì¶þ´ÎÏîϵÊý´óÓÚ0£¬ËùÒÔ¿ª¿ÚÏòÉÏ£¬ËùÒÔ¶þ´Îº¯Êý¶¨ÒåÓòΪrºã³ÉÁ¢¡£
ÔõÑùÖ¤Ã÷:µ±¶þ´Îº¯ÊýͼÏñÔÚxÖáÒÔÉÏʱµÂ¶ûËþСÓÚÁã?
12Â¥£ºÄäÃûÓû§
ÓëxÖáûÓн»µã£¬½èÖúͼÏñºÜÈÝÒ×Àí½â¡£
1¡¢¶þ´Îº¯ÊýͼÏñÔÚxÖáÉÏ·½Ê±£¬
¼´y=ax+bx+cÖÐa£¾0£¬Í¼Ïñ¿ª¿ÚÏòÉÏ£¬ÇÒͼÏñÓëxÖáûÓн»µã£¬Ò²¾ÍÒâζ×ÅÒ»Ôª¶þ´Î·½³Ìax+bx+c=0ÎÞʵÊý¸ù£¬Åбðʽ¡÷=b-4ac£¼0£»
2¡¢Í¬Àí£¬
¶þ´Îº¯ÊýͼÏñÔÚxÖáÏ·½Ê±£¬
¼´y=ax+bx+cÖÐa£¼0£¬Í¼Ïñ¿ª¿ÚÏòÏ£¬ÇÒͼÏñÓëxÖáûÓн»µã£¬Ò²¾ÍÒâζ×ÅÒ»Ôª¶þ´Î·½³Ìax+bx+c=0ÎÞʵÊý¸ù£¬Åбðʽ¡÷=b-4ac£¼0¡£
ËùÒÔ¶þ´Îº¯ÊýͼÏñÔÚxÖáÉÏ·½»òÏ·½Ê±£¨¼´ÓëxÖáûÓн»µã£©£¬¡÷=b-4ac¶¼Ð¡ÓÚÁ㣻
˳±ãС½á
¶þ´Îº¯ÊýͼÏñÓëxÖáÓн»µã£¬Ôò¡÷=b-4ac¡Ý0£º
¢Ù¶þ´Îº¯ÊýͼÏñÓëxÖáÖ»ÓÐÒ»¸ö½»µãʱ£¬¡÷=b-4ac=0£»
¢Ú¶þ´Îº¯ÊýͼÏñÓëxÖáÓÐÁ½¸ö½»µãʱ£¬¡÷=b-4ac£¾0¡£
Ï£Íû¶ÔÄãÓаïÖú£¡
13Â¥£ºÈôÐÀÓ£Çç
ͼÏñÔÚxÖáÒÔÉϱØÐ뿪¿ÚÏòÉÏ£¬ËùÒÔa£¾0¡£¶¥µã×ø±ê£¨-b/2a£¬-¦Ä/4a£©£¬¶ø¶¥µã±ØÔÚxÖáÉÏ·½£¬ËùÒÔ×Ý×ø±ê£¾0£¬ËùÒÔ-¦Ä/4a£¾0£¬ÓÖa´óÓÚ0£¬ËùÒÔ¦ÄСÓÚ0
14Â¥£ºË¿Óò
µ±¶þ´Îº¯ÊýͼÏñÔÚxÖáÉÏ·½ËµÃ÷Å×ÎïÏßÓëxÖáÎÞ½»µã
¿ÉÒÔÍƳöÅбðʽ£¼0£¬ÅбðʽÄã¿ÉÒÔд³öÈ«²¿µÄ¹«Ê½·¨À´ËµÃ÷Ò²¿ÉÒÔ²»Ð´
²»ÂÛxΪºÎʵÊý£¬¶þ´Îº¯Êýy=ax2-2x+cµÄÖµºãΪ¸ºÊýµÄÌõ¼þÊÇ______
15Â¥£ºÊÖ»úÓû§
¸ù¾Ý¶þ´Îº¯ÊýÓëxÖá½»µãÐÔÖʵóö£º
£¨-2£©2-4ac£¼0£¬ÇÒa£¼0ʱ£¬²»ÂÛxΪºÎÖµ£¬º¯Êýy=ax2+bx+c£¨a¡Ù0£©µÄÖµºãСÓÚ0£¬
½âµÃ£ºa£¼0£¬ac£¾1£®
¹Ê´ð°¸ÊÇ£ºa£¼0£¬ac£¾1£®
¶þ´Îº¯ÊýµÄֵΪ¸ºÊýµÄÌõ¼þ£¿
16Â¥£ºÄäÃûÓû§
da£¼0,¶þ´Îº¯Êý¿ª¿ÚÏòÏ£¬ÓÐ×î´óÖµ£»
¡÷=b^2-4ac<0,¶þ´Îº¯ÊýÓëxÖáÎÞ½»µã£¬¼´¶þ´Îº¯ÊýµÄ×î´óֵСÓÚ0£¬´Ëʱ¶þ´Îº¯ÊýµÄÖµºãΪ¸ºÊý¡£
17Â¥£ºÂäÔµ8Á÷˼
yΪ¸º ÔòÔÚxÖáÏ·½ ÓëxÖáÎÞ½»µãÔòb^2-4ac<0
yÔÚxÖáÏ·½ Ôò¿ª¿ÚÏòÏÂa<0 Ñ¡d
18Â¥£º³Â־ǿôÎôλ¨
Ñ¡d°É¡£¸ù¾ÝÇó¸ù¹«Ê½¿ÉÒÔËã
Äã´úÌØÊâÖµÒ²ÐÐ
19Â¥£ºÄäÃûÓû§
¿ª¿ÚÏòÏ£¬ÓëxÖáûÓн»µãÑ¡d
µÂ¶ûËþµÄº¬Òå £¬ÔÚ Ê²Ã´Ê±ºò£¬µÂ¶ûËþСÓÚÁ㣬ʲôʱºò´óÓÚÁ㣬ʲôʱºòµÈÓÚÁ㣬º¯ÊýµÄ¾ßÌåÒâÒå
20Â¥£ºÎçºóÀ¶É½
¡÷£½0£¬Ò»Ôª¶þ´Î·½³ÌÓÐÁ½¸öÏàµÈµÄʵÊý¸ù
¡÷£¾0£¬Ò»Ôª¶þ´Î·½³ÌÓÐÁ½¸ö²»ÏàµÈµÄʵÊý¸ù
¡÷£¼0£¬Ò»Ôª¶þ´Î·½³ÌûÓÐʵÊý¸ù
21Â¥£ºÓÀÔ¶µÄ
²»Ì«Çå³þÄãÎʵÄÊÇʲô¡¡
¶ÔÓÚ¶þ´Îº¯Êýy=ax^2+bx+c,(a¡Ù0)ºÍÒ»Ôª¶þ´Î·½³Ìax^2+bx+c=0£¬(a¡Ù0)delta=b^2-4ac
´óÓÚÁ㻹ÊÇСÓÚÁ㣬Ëã³öÀ´¾ÍÖªµÀÁË°¡
dalta>0ʱ£¬¶þ´Îº¯ÊýµÄͼÏñÓëxÖáÓÐÁ½¸ö²»Í¬µÄ½»µãdelta=0ʱ£¬¶þ´Îº¯ÊýµÄͼÏñÓëxÖáÓÐÒ»¸ö½»µãdelta<0ʱ£¬¶þ´Îº¯ÊýµÄͼÏñÓëxÖáûÓн»µã
¸ßÖÐÊýѧ£¬µÚÆßÌ⣬Çó½â£¬Ð»Ð»£¬£¬£¬£¬ÎªÊ²Ã´µÂ¶ûËþСÓÚÁ㣬£¬¾ßÌå½²½â£¬Ð»Ð»
22Â¥£º²»×·Å®µÄ
ÕâÒª·ÖÁ½ÖÖÇé¿öÌÖÂÛbai£º
µ±m=0ʱ£¬duy=1/8£¬´Ëʱ¶¨ÒåÓòҲΪr£»
µ±m¡Ùzhi0ʱ£¬ÒªÊ¹µÃ·Ödaoĸ¡Ù0£¬Ôò±Ø»ØÐëʹ·½³Ì¡°·Öĸ=0¡±ÎÞ´ð
ʵÊý¸ù½â£¬ÕâÊÇÒ»¸öÒ»Ôª¶þ´Î·½³Ì£¬ÒªÊ¹ËüÎÞʵÊý¸ù£¬¾Í±ØÐëµÂ¶ûËþ<0½á¹ûÒª°ÑÕâÁ½ÖÖÇé¿ö×ö¸ö²¢¼¯
23Â¥£ºÒ¹À»ÃαÊ
ÄãÒѾ֪µÀm=0ÎÞ½â¶Ô°É
m²»µÈÓÚ0ʱ
°Ñʽ×ӱ任һÏÂ
mx^2-6mx+m+8=1/y
×ó²àΪһ¶þ´Îº¯Êý µ±µÂ¶ûËþ¡·=0ʱ »áÈûط½³ÌÓнâ´ðÒ²¾ÍÊÇ´ÓͼÏñÉÏ¿´ÓëxÖáÓн»µãʹµÈʽΪ0
ºÜÃ÷ÏÔÓҲ಻»áµÈÓÚ0
ËùÒÔʹµÂ¶ûËþ<0 ÈÃÆ䷶Χ²»ÓëxÖáÏཻ
24Â¥£ººÇºÇ
m´óÓÚÁãʱ£¬µÂ¶ûËþ´óÓÚÁã¾ÍÎÞ½âÁË£¬µÂ¶ûËþСÓÚÁã²ÅÓнâ
25Â¥£ºÇóÎä¶Èħ
²»¶Ô°ÉÎÒÔõôËãÊÇ0СÓÚmСÓÚ1ÄØ