题干

已知:关于x的方程x2+(2-m)x-2m=0.
⑴求证:无论m取什么实数值,方程总有实数根;
⑵取一个m的值,使得方程两根均为整数,并求出方程的两根。

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答案(点此获取答案解析)

解:(1)△=(2-m)2-4×2m=(m-2)2≥0,所以方程总有实数根;
(2)当m=0时,原方程化为:x2+2x=0,
x(x+2)=0,
解得x=0或-2.

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