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For which value of p² does the equation y² + xy + px² − x − 2y + p = 0 represent a pair of straight lines?

1. 2
2. 2/3
3. 1/4
4. 1/2

Correct answer: 1/4

Solution

For a pair of lines, the determinant condition with a=p, b=1, h=1/2, g=-1/2, f=-1, c=p gives p^2 - (5/4)p + 1/4 = 0 -> p=1/4 or p=1. The valid value listed is 1/4.

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