Mark the correct statement(s) 

Let $K\in N,K>3,1+x^k+x^{2k}=\prod _{i=1}^k(1+a_{i}x+x^2)$ then the value of  $\frac{1}{K}\sum _{i=1}^k{a}_i^2$   is 2.

Coefficient of  $x^{100}$  in ${(\text{1}+\text{x}+{\text{x}}^2+\mathrm{...}+x^{100})}^3$ is 5050

define  $P_0\left(x\right)=x-2,P_K\left(x\right)=P_{K-1}^2\left(x\right)-2,K\ge 1$ , if the coefficient of $x^2$  in $P_k\left(x\right)$  is  $a.b^k+c.d^k$ $(b > d)$, then $\frac{(a+b+c)}{d}=4$

For any integer  $n\ge 7$, the minimum value of the polynomial $P_n\left(x\right)=x^{2n}+2x^{2n-1}+3x^{2n-2}+\mathrm{....}+(2n-1)x^2+2nx$  on set of all real numbers is ‘-n’.