2023高三·全国·专题练习
1 . 证明实系数奇数次多项式必有一实数根.
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2 . 设a,b,c,d是方程
的4个复根,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fb1f12aa4b7bb3fdb6e6ffe9ed6620f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/572de66c177f46a541e594449b688e46.png)
A.![]() | B.![]() | C.![]() | D.前三个答案都不对 |
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3 . 设
、
是无穷复数数列,满足对任意正整数n,关于x的方程
的两个复根恰为
、
(当两根相等时
).若数列
恒为常数,证明:
(1)
;
(2)数列
恒为常数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80289c798034033f2f7cfcd7590f2344.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3002f56900c2924bfd79fc3865b0a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52cabfa2464501decf05aed007cbaf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/841f4ea50fa0c2b4c6e47dc04597abba.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/561d594ed04e6652c75dac56259f4292.png)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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4 . 设p,q均为不超过100的正整数,则有有理根的多项式
的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6e8992253b0acad898a064c8ab086ce.png)
A.99 | B.133 | C.150 | D.前三个答案都不对 |
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5 . 求所有正整数
,满足正
边形能内接于平面直角坐标系
中椭圆
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8715a3f984d2627afd7c40c61347b7cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
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6 . 已知多项式
有2020个非零实根(可以有重根),其中
为非负整数,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbe0f88b114be7f35811e14c72efe145.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e813e74e0aa1ade90df848cf50773443.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1be670ec5010ca756dba19a8e4799557.png)
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