1.10.15 Polynomials
condition: Find the coefficients \( A, B, C, D \) for which the polynomial \( f(x)=x^{4}+A x^{3}+ \) \( +B x^{2}-8 x+4 \) will be the perfect square of the polynomial \( \varphi(x)=x^{2}+C x+D \).
Polynomials and their complex, real and rational roots. Decomposition in various numerical fields.