题目内容
已知关于
的方程
在区间
上有实数根,则实数
的取值范围是
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202349757271.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202349773911.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202349789390.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202349804287.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202349789390.png)
当
时,方程为
,解得
,符合;
当
时,记
,其中
。当
时,
,所以题目条件等价于函数
在区间
内有零点。
当
时有函数对称轴
,若
,即
,此时
的零点为
,不符合。因为
,
,即
,所以可知对称轴
,画图可知此时
在区间
内无零点。
当
时有函数对称轴
,此时
恒成立。因为
,所以有
,解得
。所以此时![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202350319470.png)
综上可得,![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202350335466.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202349835369.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202349851653.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202349867332.png)
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202349882403.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202349913789.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202349929635.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202349945503.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202349960822.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202349913789.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202349991383.png)
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202350007398.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202350023627.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202350038589.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202350069459.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202350085891.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202350101424.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202350116681.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202350132618.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202350147475.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202350163627.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202350179502.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202349991383.png)
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202350225387.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202350241615.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202350132618.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202350272672.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202350288633.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202350303381.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202350319470.png)
综上可得,
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823202350335466.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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