配套习题- 如何确定一元二次方程的整数解（一） -【青果学院】

1/5单选题

难度：

1.已知：关于x的一元二次方程mx²-3（m-1）x+2m-3=0若m为整数，且方程的两个根均为正整数，求m的值（）

A	m=-1或m=-3
B	m=-1
C	m=-3
D	m=-2

正确答案：QQ==

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

2/5单选题

难度：

2.关于x的一元二次方程（m-1）x²-2mx+m+1=0. 整数m为（）时，此方程的两个根都为正整数.

A	m=2
B	m=3
C	m=-3
D	m=2或m=3

正确答案：RA==

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

3/5单选题

难度：

3.已知关于x的一元二次方程（m²-1）x²-6（3m-1）x+72=0. 求整数m是（）时，此方程有两个不相等的正整数根？

A	m=±1
B	m=2
C	m=3
D	m=4

正确答案：Qg==

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

4/5单选题

难度：

4.关于x的一元二次方程mx²-（m+3）x+3=0有两个不相等的实数根，若m为正整数，设方程的两个整数根分别为p，q（p＜q），则点P（p，q）的坐标（）

A	（-1，-3）
B	（1，3）
C	（1，-3）
D	（-1，3）

正确答案：Qg==

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

5/5单选题

难度：

5.已知关于x的一元二次方程x²+2x+2k-4=0有两个不相等的实数根若k为正整数，且该方程的根都是整数，求k的值（）

A	5
B	4
C	3
D	2

正确答案：RA==

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