The question is
Let $a$$,b$$,c$$,d$ be any four real number not all equal to zero. Prove that the roots of the polynomial $f(x)=x^6+ax^3+bx^2+cx+d$ cannot all be real.
I know that the first derivative of a functions gives its turning points and the second derivative give its concavity but how does it help to solve the question. Or if you have any other methods it would really help.Any hint would also be appreciated . Thanks in advance.