How many roots does the polynomial $acx^4 + b(a + c)x^3 + (a^2 + b^2 + c^2)x^2 + b(a + c)x + ac$ have Let a, b and c be real numbers. Then the fourth degree
polynomial in $x$, $acx^4 + b(a + c)x^3 + (a^2 + b^2 + c^2)x^2 + b(a + c)x + ac$
(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
I have no clue as to how to approach it, a hint would suffice

HINT: write your equation in the form
$$(x(ax+b)+c)(a+x(b+cx))=0$$ and solve it
