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Find the value of lamda so that the equa...

Find the value of `lamda` so that the equations `x^(2)-x-12=0` and `lamdax^(2)+10x+3=0` may have one root in common. Also, find the common root.

Text Solution

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`:'x^(2)-x-12=0`
`implies(x-4)(x+3)=0`
`:.x=4,-3`
If `x=4` is a common root then
`lamda(4)^(2)+10(4)+3=0`
`:.lamda=-43/16`
And if `x=-3` is a common root then
`lamda(-3)^(2)+10(-3)+3=0`
`:.lamda=3`
Hence for `lamda=-43/16` common root is `x=4`
and for `lamda=3`, common root is `x=-3`.
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