5. The condition for 3x² + 2pxy + 2y2 + 2ax - 4y + 1 can be resolved into two linear factors then k is
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Answer:-
For the condition to be true , the roots of the equation must be rational.
⟹−2αy+2a±D/ √2 must give rational roots.
For the above expression to give rational roots, D must be a perfect square of a rational number.
⟹4(α2−2)y2+(2aα+4)y+a2−1 should be a perfect square.
⟹ The discriminant of above expression =0. By doing that, we get our required result.
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