How to solve x2-3x 4 = 0

How to solve x2-3x 4 = 0

x²-3x-4=0
x²-（4-1）x-4×1=0
（x+1）（x-4）=0
X = - 1 or x = 4

Given X4 + X3 + x2 + X + 1 = 0, find the value of 1 + X + x2 +... + x2010

Answer: 1 + X + x2 +... + x2010 = 1 + X + x2 + X3 + X4 + X5 (1 + X + x2 + X3 + X + x4) + x10 (1 + X + x2 + X3 + x4)... + x2005 (1 + X + x2 + X3 + x4) + x2010 = x2010x4 + X3 + x2 + x2 + X + 1 = 0, multiply both sides by (x-1), get: (x4 + X3 + x2 + X + 1) (x-1) = x5-1 = 0, so X5 = 1, so x2010 = (x5) ^ 402 = 1 ^ 402 = 1

Given X4 + X3 + x2 + X + 1 = 0, find the value of 1 + X + x2 +... + X2009

This is the first + X + X + X + X + X \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\;) (i.e. group of five) = 0 prompt: from the first item