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If the determinant expression [a, b, ax+by; b, c, bx+cy; ax+by, bx+cy, 0] is considered under the conditions b²-ac<0 and a<0, what is its sign?

1. Zero
2. Positive
3. Negative
4. b²+ac

Correct answer: Positive

Solution

The determinant is positive because the conditions given, specifically that the quadratic form defined by the matrix is negative definite due to the inequality, imply that the overall determinant must be positive when evaluated.

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