Prove that for an arbitrary pair of vectors
![f](/media/m/9/9/8/99891073047c7d6941fc8c6a39a75cf2.png)
and
![g](/media/m/9/5/8/958b2ae8c90cadb8c953ce50efb9c02a.png)
in the space the inequality
holds if and only if the following conditions are fulfilled:
%V0
Prove that for an arbitrary pair of vectors $f$ and $g$ in the space the inequality
$$af^2 + bfg +cg^2 \geq 0$$
holds if and only if the following conditions are fulfilled:
$$a \geq 0, \quad c \geq 0, \quad 4ac \geq b^2.$$