The condition for the polynomial equation of degree 4 ax^4+bx^2+c=0 to have four distinct real roots is
b^2-4ac>0
b^2-4ac<0
b<0 and b^2-4ac>0
b<0, b^2-4ac>0 and ac>0
The quartic equation ax^4+bx^2+c=0 can be taken as a quadratic equation in terms of x^2, of which the roots can be determined by the root formula
In order for x^2 to have real roots, the discriminant must be great than 0, then
In order for x to have 4 distinct real roots, x^2 must be a positive real number, then we get
Then we get
So choice D is the correct.
PS: it's also possible for the equation has all real roots when b^2-4ac=0 and b<0 (a>0), then the equation has 2 pair of equal real roots (not distinct 4 real roots).