Given that (x-3) and (2x+1) are factors of

$\displaystyle f(x)=ax^4+bx^3+13x^2=30x+9$, find the values of a and b . With these values of a and b , show that $\displaystyle f(x)\geq0$ for all x belongs to real numbers .

My working :

i found that a = 4 and b = -20

$\displaystyle 4x^4-20x^3+13x^2+30x+9$

$\displaystyle (x-3)(2x+1)(2x^2-5x-3)$

I am wondering how can i show that $\displaystyle f(x)\geq0$ from here .

Thanks for any help .