Let $a, b$ and $c$ be real numbers. Then the fourth degree polynomial in $x,\boxed{ a c x^{4}+b(a+c) x^{3}+\left(a^{2}+b^{2}+c^{2}\right) x^{2}+b(a+c) x+ ac}$
(a) Has four complex (non-real) roots
(b) Has either four real roots or four complex roots
(c) Has two real roots and two complex roots
(d) Has four real roots
My approach
Let $t_1,t_2,t_3,t_4$ be the roots of the equation:-
1)$t_1+t_2+t_3+t_4$= $\frac{-b(a+c)}{ac}$= real number
2)$t_1t_2+t_2t_3+t_3t_4+t_1t_3+t_1t_4+t_2t_4$=$\frac{(a^2+b^2+c^2)}{ac}$)=real number
so (b) will be the option