If a, b and c (a > 0, c > 0) are in GP, then consider the following in respect of the equation \( ax^{2} + bx + c = 0 \):
1. The equation has imaginary roots.
2. The ratio of the roots of the equation is \( 1 : \omega \) where \( \omega \) is a cube root of unity.
3. The product of roots of the equation is \( \frac{b^{2}}{a^{2}} \).
Which of the statements given above are correct?
If \( x^{2} + mx + n \) is an integer for all integral values of x, then which of the following is/are correct?
1. m must be an integer
2. n must be an integer
Select the correct answer using the code given below.
If in a triangle ABC, \( \sin^{3} A + \sin^{3} B + \sin^{3} C = 3\sin A \sin B \sin C \), then what is the value of the determinant \( \begin{vmatrix} a & b & c \\ b & c & a \\ c & a & b \end{vmatrix} \), where a, b, c are sides of the triangle?
