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If equation (lamda^(2)-5lamda+6)x^(2)+(l...

If equation `(lamda^(2)-5lamda+6)x^(2)+(lamda^(2)-3lamda+2)x+(lamda^(2)-4)=0` is satisfied by more than two values of `x`, find the parameter `lamda`.

Text Solution

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If an equation of degree to is satisfied by more than two values of unknown, then it must be an identity. Then, we must have
`lamda^(2)-5lamda+6=0,lamda^(2)-3lamda+2=0lamda^(2)-4=0`
`implieslamda=2,3` and `lamda=2,1` and `lamda=2,-2`
Common value of `lamda` which satisfies each condition is `lamda=2`.
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