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If the equation 4y^(3) - 8a^(2)yx^(2) - ...

If the equation `4y^(3) - 8a^(2)yx^(2) - 3ay^(2)x +8x^(3) = 0` represents three straight lines, two of them are perpendicular, then sum of all possible values of a is equal to

A

`(3)/(8)`

B

`(-3)/(4)`

C

`(1)/(4)`

D

`-2`

Text Solution

Verified by Experts

The correct Answer is:
B
We have `4y^(3) -8a^(2)yx^(2) - 3ay^(2)x +8x^(3) =0`
`rArr 4 ((y)/(x))^(3) -3a ((y)/(x))^(2) -8a^(2) ((y)/(x)) +8 =0` has roots `m_(1),m_(2),m_(3)`
`:. m_(1)m_(2)m_(3) =- 2`
Given `m_(1)m_(2) =-1`
`:. m_(3)=2`
`:. 4(2)^(3)-3a(2)^(2) -8a^(2)(2) +8 =0`
`rArr 4a^(2) +3a - 10 =0`
`:.` Sum of possible values of roots `=(-3)/(4)`
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