JEE MainMathematicsModerateStraight Lines

If equation $4y^{3} - 8a^{2}yx^{2} - 3ay^{2}x + 8x^{3} = 0$
represents three straight lines, two of which are perpendicular to each
other, then find sum of all possible values of a.;fn lehdj.k $4y^{3} - 8a^{2}yx^{2} - 3ay^{2}x + 8x^{3} = 0$ rhu ljy
a

Show answer and solution

4m^{3} - 3am^{2} - 8a^{2}m + 8 = 0

\Rightarrow m_{1}m_{2}m_{3} = - 2

\Rightarrow m_{3} = 2

\Rightarrow 4(2)^{3} - 3a(4) - 16a^{2} + 8 = 0

\ sum\ = - \frac{12}{16}

Source: Grass-G / M-27 Mathematics Paper 2 15 Jan.docx

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