maximum and number of distinct real roots If $f(x)=x^6+2x^5+bx^4+x^3+bx^2+ax+1$ and $f(1)=0$ and $f(-1)\neq 0.$ Then maximum number of distinct real roots of $f(x)=0,$ is 


what i try: $x^6+2x^5+bx^4+x^3+bx^2+ax+1=0$

$x=0$ in not a solution 

$$x^3+\frac{1}{x^3}+\bigg(2x^2+\frac{a}{x^2}\bigg)+b\bigg(x+\frac{1}{x}\bigg)+1=0$$

How do i solve it Help me please
Hint:

If $f(1)=0$ then the sum of the even and odd coefficients differ only by sign. That is, $2b+2=-(a+3)\to a=-2b-5$
Hint:

If $f(1)=0$ then the sum of the even and odd coefficients differ only by sign. That is, $2b+2=-(a+3)\to a=-2b-5$