Abstract:
In the present paper, we investigate whether the roots of a biquadratic equation determined by a pair of real symmetric positive definite matrices of order 3 and a three-dimensional vector of parameters are real. We obtain the explicit representation of the discriminant of such a polynomial as the sum of at most two squares.
Keywords:biquadratic equation, real roots, hyperbolic polynomial, biquadratic form, trace of a matrix, skew-symmetric matrix.