北师大版九年级数学上册同步练习:2.5 一元二次方程的根与系数的关系

适用年级:初三
试卷号:607766

试卷类型:课时练习
试卷考试时间:2018/8/1

1.单选题(共5题)

1.
方程ax2+bx-c=0(a>0,b>0,c>0)的两个根的符号为(  )
A.同号B.异号C.两根都为正D.不能确定
2.
若x1,x2是一元二次方程x2-2x-3=0的两个根,则x1·x2的值是()
A.2B.-2C.4D.-3
3.
与是方程的两个根,且,则m的值为(  )
A.-1或2B.1或-2C.-2D.1
4.
已知一元二次方程的两根分别是2和-3,则这个一元二次方程是(  )
A.x2-6x+8=0B.x2+2x-3=0C.x2-x-6=0D.x2+x-6=0
5.
若x1,x2是一元二次方程x2+10x+16=0的两个根,则x1+x2的值是()
A.﹣10B.10C.﹣16D.16

2.选择题(共2题)

6.如图所示,直线L1,L2,L3相交于一点,则下列答案中,全对的一组是(   )

7.根据短文内容的理解,选择正确答案。

    In China, there're many different kinds of food. Some of them are very popular. The real Chinese food is dumplings. Now let's talk about them, OK?

    Everyone in China likes dumplings very much, and there are many different kinds of dumplings. Some have meat and vegetables in them, others have sugar, eggs and so on. I like dumplings with vegetables and pork better than any other kind.

    Usually people make dumplings at home. If you have no time to make them, you can buy them from any supermarket. Then you take them home and eat them with vinegar.

    The Spring Festival is very important in China. When it comes, we make dumplings, usually we put a coin(硬币) in a dumpling. If one eats the dumpling with the coin in it, he or she will be lucky in the year.

    In the old days, people couldn't often eat dumplings, because they were very poor. Now our country is becoming stronger and stronger, and our people are richer and richer. We can eat them very often.

    Now tell me, do you like dumplings?

    Welcome to China, and we'll invite you to eat the real Chinese food —dumplings.

3.填空题(共2题)

8.
(题文)已知x1  , x2是关于x的一元二次方程x2﹣5x+a=0的两个实数根,且x12﹣x22=10,则a=____.
9.
已知是关于x的一元二次方程x2+(2m+3)x+m2=0的两个不相等的实数根,且满足=﹣1,则m的值是____.

4.解答题(共5题)

10.
已知关于x的一元二次方程x2+(2k-1)x+k2+1=0,如果方程的两根之和等于两根之积,求k的值.
11.
若关于x的方程x2+6x+m=0的一个根为3﹣,求方程的另一个根及m的值.
12.
已知x1,x2 是关于x的一元二次方程x2-2(m+1)x+m2+5=0的两实数根.
(1)若(x1-1)(x2 -1)=28,求m的值;
(2)已知等腰△ABC的一边长为7,若x1,x2恰好是△ABC另外两边的边长,求这个三角形的周长.
13.
已知 是关于x的一元二次方程 的两个不相等的实数根,且满足 ,求m的值.
14.
已知关于x的方程x2-(2k-1)x+k2-2k+3=0有两个不相等的实数根.
(1)求实数k的取值范围.
(2)设方程的两个实数根分别为x1,x2,是否存在这样的实数k,使得|x1|-|x2|=成立?若存在,求出这样的k值;若不存在,请说明理由.
试卷分析
  • 【1】题量占比

    单选题:(5道)

    选择题:(2道)

    填空题:(2道)

    解答题:(5道)

  • 【2】:难度分析

    1星难题:0

    2星难题:0

    3星难题:0

    4星难题:1

    5星难题:0

    6星难题:5

    7星难题:0

    8星难题:5

    9星难题:1