If , and are three polynomials of degree 2, then prove that is a constant…

MATHEMATICS · Subjective · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

f(x)

g(x)

and

h(x)

are three polynomials of degree 2, then prove that

\eta(x) = \left|\begin{matrix} f(x) & g(x) & h(x) \\ f'(x) & g'(x) & h'(x) \\ f''(x) & g''(x) & h''(x) \end{matrix}\right|

is a constant polynomial.