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1、一元二次方程专项解析训练（七）【例题精选】例1 不解方程，判断下列方程的根的情况解：（1）中，注意：使用根的判别式时必须把方程化为一般形式；弄清楚方程中字母系数的符号例2 k取什么值时，方程（1）有两个不相等的实数根；（2）有两个相等的实数根；（3）没有实数根解：（1），（2），（3）例3 若关于x的方程有两个实数根，求a的取值范围解：当，方程有两个实数根注意：二次项系数是字母时，一定要注意一元二次方程的根的判别式是二次项系数的情况下运用的所以由D的符号求出m的范围必须将m=0的情况排除掉例4 求证：m为任何实数时，方程有两个不相等的实数根分析：欲证方程有两个不相等的实数根，即要证证明： 为任
2、何实数时，方程都有两个不相等的实数根注意：计算出无法直接说明，必须经过适当的变形使之确实大于0此处符号的判断采用配方成完全平方式后，用非负数性质来判定有时也需要把代数式进行因式分解化成乘积的形式，利用“同号得正，异号得负”来判定例5 已知： 方程一根为2，求它的另一个根及p的值分析：利用一元二次方程根与系数的关系可以得到关于方程两根及系数中字母的方程组，通过解方程组即可求得另一根及字母的值解：设方程一根为由根与系数的关系，得：例6 方程，求：（1）（2）（3）（4）（5）（6）分析：运用一元二次方程根与系数的关系，可以求出两根之和与两根之积，即故应把所求代数式通过恒等变形得到含有的代数式解：由
3、根与系数的关系：（2）（4）（5）（6）注意：在（3）（4）（5）题中的可利用（2）题的结果，但前提条件是前面的每一步计算应准确无误例7 求作一个一元二次方程，使它的两根为分析：考虑一元二次方程的一般形式：首先把二次项系数化为1，得：设这个一元二次方程的两根为根据根与系数的关系：即：使二次项系数为1，两根之和的相反数作为一次项系数，两根之积作为常数项解：，注意：一般求作的方程均设二次项系数为1，若其它系数为分数时，最后方程均应化为整数系数方程如：例8 求作一个一元二次方程，使它的两根分别为方程的两根的倒数分析：为了与原方程有所区别，设所求方程为关于y的方程，则设两根为关键是要求出的值解：设方程
4、例9在实数范围内分解因式：（1）（2）（3）（4）解：（1）（2）（3）（4）例10k为何值时，二次三项式可因式分解解：方程即当时，二次三项式可因式分解【专项训练】一、不解方程，判断下列方程的根的情况1、2、3、4、5、6、二、填空题1、如果一元二次方程有两个相等的实数根，那么2、一元二次方程有实数根，那么a的取值范围是3、若二次方程没有实数根，那么a4、方程的两根的和是，两根的积是5、方程的两根的平方和是，两根差的平方是6、一元二次方程的两根分别是，则这个方程是7、方程8、设的两个根，那么三、选择题：1、已知关于x的方程，那么根的情况是（ ）A不论m取何值，方程都有两个不相等的实数根B不论m
5、取何值，方程都有两个相等的实数根C不论m取何值，方程都没有实数根D只有m取某些值时，方程才有实数根2、方程有实数根，则必须（ ）AB CD 3、 方程那么另一根是（ ）AB C D以上答案都不对4、若方程的两根中只有一个根为0，那么（ ）A B C D 5、设 的值是（ ）A B C D 6、以3和2为根的一元二次方程是（ ）AB CD 7、两个实数根的和是3的一元二次方程是（ ）AB CD 8、两根均为负数的一元二次方程是（ ）A B C D 四、已知关于取何值时，（1）方程有两个不相等的实数根；（2）方程有两个相等的实数根；（3）方程没有实数根五、k取什么值时，方程 有两个相等的实数根，并
6、求出这时方程的根六、求证：关于x的方程有两个不相等的实数根七、已知：关于x的方程的两根为，求m的值八、不解方程，作一个一元二次方程，使它的两根（1）分别是方程 的两根的立方（2）分别是方程的两根的3倍；（3）分别是方程 的两根平方的负倒数九、二次三项式的因式分解（1）（2）（3）（4）（5）（6）（7）（8）（9）（10）（11）（12）【答案】一、1、两不等实根2、无实根3、两不等实根4、两相等实根5、两不等实根6、无实根二、1、 2、 3、 4、 5、 6、 7、 8、 三、1、A2、D3、C4、C5、C6、C7、C8、C四、（1）五、 六、 七、 八、（1） （2） （3） 九、二次三项
7、式的因式分解（1）（2）（3）（4）（5）（6）（7）（8）（9）（10）（11）（12）（英文版 ） easily blame, to prevent the broken window effect. Supervise the leading cadres to play an exemplary role, take the lead in the strict implementation of the and , lead to safeguard the solemnity and authority of the party discipline, ensure that th
8、e party discipline and the laws and regulations for implementation in place. Throughout the discipline in the daily supervision and management, strengthen supervision and inspection, from the thorough investigation of violations of discipline behavior. Strengthen to key areas, key departments and ke
9、y projects as well as the masses reflect the concentration of the units and departments for supervision. - strengthening supervision, discipline inspection and supervision of cadres to set an example for compliance with the and is a man must be hexyl, blacksmith needs its own hardware. Discipline in
10、spection organs as the executor of the party discipline, and supervisor of the defenders, for its supervision must be more strictly, discipline inspection and supervision of cadres to firmly establish the awareness of Party Constitution, sense of discipline and rules consciousness, politics loyalty,
11、 sense obey. Action speak Ji Ordinance to set an example of the regulations of the rule of law, strengthen supervision and accept the supervision of the firmness and consciousness, do comply with and . To firmly establish the discipline must first be disciplined, the supervisor will be subject to th
12、e supervision of concept, and consciously safeguard and implement party compasses party, take the lead in practicing three strict real strict, so loyal, clean, play. To be good at learning, the Constitution and the as morality, politics and brought to fruition; to implement , do not want to, dare no
13、t, not with disciplinary ruler to supervision; to discipline a ruler, often the control inspection, and consciously in the ideological red line to draw the row Ming Good accumulation is indeed the bottom line, so that the heart has fear, said to have quit, the line has ended. Attached: indifferent t
14、o heart, calmly to the table in our life, there are many unpredictable things will happen, some good, some bad things, we cannot control is powerless to stop, but with time, you will find in life sometimes turns out to be not good, some bad things finally turned out to be a good thing, but then we m
15、uddy however did not know, this is the life teach us things. 1, life can be complex, can also be simple. Want simple life of precipitation, to have enough time to reflect, to make Become more perfect. Life is the most important thing is not to win, but the struggle; not to have conquered, but to hav
16、e fought well. 2, the plain is the background of life. Live a plain life, give up on themselves is not a coward, but the wise answers; not disillusioned after the heart, such as ashes, but experience the storm after the enlightenment; not unrewarding perfunctorily, but calm attitude of life of unres
17、trained self-confidence. Plain living, there is no noise noisy, no earthly troubles, more did not fill in the discontent of desire, some just a calm, a calm. 3, memory of heart will not good things to erase the, life is a When no movie, pain is a beginning, the struggle is a kind of process, death i
18、s a kind of ending. Give up this giving up is the helpless, do not give up the abandoned, do not give up this giving up is ignorance, do not give up should not give up is persistent. 4, a thing figured is heaven, think impassability is hell. Since the living, to live better. Sometimes we because of
19、too narrow-minded, too care around the chores and penny wise and pound foolish, not worth the candle. Some things to attract trouble and worry, completely depends on how we look at and deal with it. Dont always take everything back to things, and dont get into a blind alley, dont want to face, dont
20、be narrow-minded. Poke to care, is a kind of open-minded, a free and easy. 5, I am not afraid of others behind me a knife, I afraid to look back and see stab me, is my intention to treat people; I am not afraid of the truth to tell the best friend, Im afraid he turned to it as a joke to tell dont 6,
21、 when we are in a positive frame of mind, you will find many good things; and when we are in a negative state of mind, you will find many depressed things; life happy and worry, all is you of life attitude, optimistic, good luck; loss of sink, Eritrea company. When you are in adversity, may wish to
22、change a point of view to think everything over to the good Think, because good mentality decided the fate of the! 7, people are tired, rest; heart tired, calm. Grow up, mature, this society read. Tired and sad, squat down, to their a hug. Because the world no one can sympathize with you, have mercy
23、 on you. You cry, tears is your own; you pain, no one can understand. Then you only tears to smile. 8, each people have youth,Each youth are a story, the life of the world never gets easier, I want what, wish the world all know, as has been the same; now want anything, for fear that others know, or
24、like to lose the same. 9, the heart move, everything in the world is followed by birth, Rangrang, important thing is often the most difficult to open ones mouth, because words will reduce its importance; to let strangers people care about your life in the good things, the original is not easy 10, do
25、 not blame, do not laugh at who, also dont envy who. Like a person is a kind of feeling, not like a person is true. The truth is easy to explain, I feel Is unspeakable. The best travel life is that you in a strange place found a long lost touched. 11, happy life not in the bustling in, and in the pe
26、ace of mind; no matter how many grievances, how uncomfortable, and ultimately to heal themselves or their own, others may got you to comfort, but never know your heart is how wanjianchuanxin. 12, maam, like a movie, learn to appreciate, learn to be grateful, learn tolerance, and goodness, helping ot
27、hers. Instead of accusing the society, as into one; and an exception is better to give than to what 13, dont envy him A sum of, dont lose your life and the life, respectively is: the former is a we experienced cannot escape in a day finally will last minute, while the latter is our persistent, we wa
28、nt to cherish the memory of those people and things. 14, learn to smile, learn to strong, the world you know so many people, so many people and you are, you cannot change also cant let everyone like you, so also do not want to do. Life is too short to go crazy to love to go to waste, to chase the dr
29、eam to regret. 15, when temper, a blessing to go. A wounding elegant people, the key is to control their own emotions. With the mouth is the most stupid behavior. A control negative emotions than a can take a city more powerful water flow slow, language is expensive. People spent two years of time t
30、o learn to speak, but to spend a few years time to shut up. That is a kind of ability, that is a kind of wisdom. 16, life is not perfect, sometimes, growth is not a cry, not an eyeful of tears, there is no trace of emotion, there is no gleam of hope, no desire, no action, no static, there is only on
31、e kind of downward sinking feeling, sink A murky? 6? 7? 6? 7 sink? 6? 7? 6? 7 toward the bottom of the sink. 17, in some way, do not go, you will not know the other side scenery is beautiful. To you is not good, you do not mind too much, no one has an obligation to you; you learn knowledge, is you h
32、ave weapons, you can start from scratch, but not unarmed; how do you treat people, does not represent how others treat you, if cannot see through this point, only inviting worry. 18, time is like a sponge in the water, as long as you are willing to squeeze, the total water is still there. Every life
33、, after the ups and downs The best test of live, to life, survival and continuation, do not stop the struggle in the joys and sorrows of life on the road, so that different soul to bear life beat, acceptance of suffering. 19, indifferent to heart, calmly in table, elegant and comfortable life, do no
34、t take what is so important. The pursuit will be disappointed; to be alive, you will have trouble. Life is the most afraid of what all want to care about, but also what all grasp is not firm, without scenery, separated populations, such as not to desire, all docked in the fate of the end. Why is too
35、 rigid, the natural, to go stay not to live, let go of obsession, revel is 20, if the fate of the broken Hopes of sailing, please dont despair, the coast is still, if the fate of the withered petals of the beautiful, please do not sink, the spring is still, life will always be endless trouble, pleas
36、e dont helpless, because they are still alive, is still a dream, the sun still, we still. Lost, keep memories; to get, must work to; but the most important is good to cherish their own. 21, life, select the complex, is to choose the pain; choose a simple, is choose to be happy. The complex world lik
37、e aSignificance of pride. Hope is the ornate palace, outside people admiring the magnificent, living in the deep knowledge of living it to pay the price. Simple world as a simple log cabin outside ridiculed shabby, the heart is willing to go live to know the joy. Suffering and joy is their own choic
38、e. 22, learn how to use a single powerful heart, let the past be the past, let the future come. Life is really the end of the end of an eagle is flying wings, life is constantly pursuit. Dont miss to regret, dont wait for old just miss. Time to return, seize every moment, again painstakingly again t
39、ired also Those struggling to fly. 23, life could not Yimapingchuan, even flat pavement, inevitably there will be a few pieces of roadblocks. Some of the rocks around the past, while others have to move it out. Just move others put the stone is very easy, because the stone from the appearance we can
40、 discern; difficult to myself to move away the heart of stone head. Leave time to spend with her, often reflect my heart, so as to remove your heart of stone. 24, everything does not have to be demanding, come to, everything does not have to care about, over the past; failing to do not frown, laugh
41、it laugh. Results Dont demand, do to; life is a simple, calm and peaceful. Always not to choose their own path and regret, life is like a train, the scenery and then the United States will retreat, the passage of time and encounter will eventually drifting further and further away, before is always
42、himself. 25, everyone has a weakness, weakness is true humanity. That has no weakness, a shallow person. That people think there is no weakness, mostly false. Life has shortcomings, there are shortcomings is the real life. That no one regret, or childish or numbness or Self deception. It is in toler
43、ance of weakness and so on to accept, people live happily.Hello, everyone! I am a party member. The title of my speech is: study and implement the partys two laws, doing practical play highway. 2015 October 18, the Central Committee of the Communist Party of China promulgated the implementation of t
44、he and Chinese Communist Party discipline and punishment regulations. We Heyuan male passers-by to respond positively to the call of the Central Committee of the party, earnestly organize the study party two regulations, truly grasp the essence and gist, and in their respective positions, to hold th
45、e bottom line of the discipline, build a strong ideological line of defense, with the courage to play, the courage to fight tough and fearless spirit, at the crucial moment well to complete the task, with practical action to test the study and implement effect Because of discipline in the * * * * *
46、* * * * * * story. Here, let me to cast a brick to attract jade, speak about our highway. Highway line section of the road surface transformation project, last year towards the country seized will be seized one of the items. To complete this arduous task, as a project management office director Comrade, keep in mind from the Communist Party membership, recognize and identify the bottom line, s