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If a > 0 discriminant of ax^2 + 2bx + c is -ve, then | a b ax + b | | b c bx + c | | ax + b bx + c (ax^2 + 2bx + c) | is

1. +ve
2. 0
3. -ve
4. (2) (ac - b^2) (ax^2 + 2bx + c)

Correct answer: -ve

Solution

The discriminant being negative indicates that the quadratic has no real roots, which implies that the quadratic expression is either entirely above or below the x-axis. Since a > 0, the quadratic opens upwards, meaning it is always positive. However, the determinant of the given matrix, which involves the quadratic, will yield a negative value due to the specific arrangement of its elements, leading to the conclusion that the determinant is negative.

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