已知集合A={kx2﹣8x+16=0}只有一个元素，试求实数k的值，并用列举法表示集合A．_刷题宝

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已知集合A={kx²﹣8x+16=0}只有一个元素，试求实数k的值，并用列举法表示集合A．

上一题下一题 0.0难度选择题更新时间:2018-04-08 07:06:19

答案(点此获取答案解析）

解：当k=0时，原方程变为﹣8x+16=0，x=2，此时集合A={2}；

当k≠0时要使一元二次方程kx²﹣8x+16=0有一个实根，需△=64﹣64k=0，即k=1．此时方程的解为x₁=x₂=4．集合A={4}，满足题意．

综上所述，实数k的值为0或1，当k=0时，集合A={2}；当k=1时，集合A={4}

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