Let R ^2 denote R R . Let S = (a, b, c) : a, b, c R and ax^2 + 2bxy + cy^2 > 0 for all (x, y) R ^2 - (0, 0) . Then which of the following statements is (are) TRUE?

JEE Advanced 2024 Mathematics question

Let denote . Let

S = {(a, b, c) : a, b, c and + 2bxy + > 0 for all (x, y) - \{(0, 0)\}}.

Then which of the following statements is (are) TRUE?

(A)
(B)If , then .Correct
(C)For any given , the system of linear equations , has a unique solution.Correct
(D)For any given , the system of linear equations , has a unique solution.Correct

Answer: (B),(C),(D)

The quadratic form is positive definite iff and (then also ). (A) – not in S, FALSE. (B) \frac{1}{12}b^2b^2\frac$14

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Question ID VK-034169