已知二次函数f(x)的二次项系数为a,且不等式f(x)>-2x的解集为(1,3).
(1)若方程f(x)=0的两根一个大于-3,另一个小于-3,求a的取值范围;
(2)若方程f(x)+6a=0有两个相等的实根,求f(x)的解析式.
考点分析:
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已知函数f(x)=
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102320117653500/SYS201311031023201176535016_ST/0.png)
(1)求函数f(x)的最小值和最小正周期;
(2)设△ABC的内角A、B、C的对边分别为a,b,c,且c=
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102320117653500/SYS201311031023201176535016_ST/1.png)
,f(C)=0,若向量
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102320117653500/SYS201311031023201176535016_ST/2.png)
与向量
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102320117653500/SYS201311031023201176535016_ST/3.png)
共线,求a,b的值.
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下列结论中:
①
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102320117653500/SYS201311031023201176535015_ST/0.png)
;
②已知命题p:∃x∈R,lgx=0;命题Q:∀x∈R,2
x>0,则P∧Q为假命题;
③由“|mn|=|m|•|n|”类比得到“
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102320117653500/SYS201311031023201176535015_ST/1.png)
;”
④若a>b,则ac
2>bc
2;
⑤在△ABC中,若
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102320117653500/SYS201311031023201176535015_ST/2.png)
.
其中正确结论的序号为
.
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平面向量
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102320117653500/SYS201311031023201176535014_ST/0.png)
与
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102320117653500/SYS201311031023201176535014_ST/1.png)
的夹角为60°,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102320117653500/SYS201311031023201176535014_ST/2.png)
=(2,0),|
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102320117653500/SYS201311031023201176535014_ST/3.png)
|=1 则|
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102320117653500/SYS201311031023201176535014_ST/4.png)
+2
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102320117653500/SYS201311031023201176535014_ST/5.png)
|=
.
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若不等式组
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102320117653500/SYS201311031023201176535013_ST/0.png)
所表示的平面区域被直线y=kx+4分成面积相等的两部分,则k的值为
.
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观察下列式子:
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102320117653500/SYS201311031023201176535012_ST/0.png)
,则可以猜想的结论为:当n∈N且n≥2时,恒有
.
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