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If the gradient of one of the lines x^(2...

If the gradient of one of the lines `x^(2)+hxy+2y^(2)=0` twice that of the other , then sum of possible values of h ____________.

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Let `m_(1)andm_(2)` be the slopes of the lines `x^(2)+hxy+2y^(2)=0`. Then ,
`m_(1)+m_(2)=-(h)/(2),m_(1)m_(2)=(1)/(2)`
But `m_(1)=2m_(2)` (given). Therefore,
`3m_(2)=-(h)/(2)and2m_(2)^(2)=(1)/(2)`
i.e., `m_(2)^(2)=(1)/(4)`
Also , `m_(2)=-(h)/(6)`
`:.(h^(2))/(36)=(1)/(4)orh^(2)=9orh=+-3`
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