theory of equations finding roots from given polynomial 
If the equation $x^4-4x^3+ax^2+bx+1=0$ has four positive roots then $a=\,?$ and $b=\,?$
$\textbf{A.}\,6,-4$
$\textbf{B.}\,-6,4$
$\textbf{C.}\,6,4$
$\textbf{D.}\,-6,-4$

we can replace options and check answers .. are there any other shortcuts we can use 

$$(x-x_1)(x-x_2)(x-x_3)(x-x_4)$$
$$=x^4-x^3\left(\sum_{4\ge i\ge1} x_i\right)+x^2\left(\sum_{4\ge i>j\ge1}x_ix_j\right)-x\left(\sum_{4\ge i>j>k\ge1}x_ix_jx_k\right)+x_1x_2x_3x_4 $$
If $x_i>0,1\le i\le4$ the coefficient of $x^2$ must be $>0$ and that of $x$ must be $<0$
