A polynomial question. I came across this question in my weekly test paper and didn't know how to tackle it. The question goes as follows:
$a_0,a_1,a_2....a_{34}$ are the coefficients of $x^0,x^1,x^2......x^{34}$ of the polynomial obtained on opening the parenthesis of $(1+x+x^2)^{17}$, then which is true?
$1)~a_1+a_2+.......+ a_{34}$ is even;
$2)~a_1=17$;
$3)~a_{33}=17$;
$4)~a_2=153$.
(One or more is correct)

Hint: if you plug $x=1$ in, you will get the sum of the coefficients.
The coefficients may be represented using Viete's formulas.
