Weirdo equations #3

Algebra Level 5

Let \[F(x)=\displaystyle\prod_{i=1}^{8} (x-a_i)\]

And \[G(x)= \displaystyle\prod_{i=1}^{8} (x^2-a_i)\]

Also \[K(x) = \displaystyle\prod_{i=1}^{8} (x^3-a_i)\]

Then find the least real root of

\[F(x)+G(x)+K(x) = 11223344\]


\(a_1=1,a_2=2,a_3=3,a_4=4.....a_8=8\)


Do not change the name
Original stuff
This is hard.
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