徵數學高手....X4+2X3+5X+2=0的實數解

設 x^4 + 2x^3 + 5x + 2 = (x^2 + ax + 1)(x^2 + bx + 2)= (x^4 + bx^3 + 2x^2 + ax^3 + abx^2 + 2ax + x^2 + bx + 2= x^4 + (a+b)x^3 + (ab+3)x^2 + (2a+b)x + 2比較係數 :a+b = 2 .....(1)
ab+3 = 0
2a+b = 5 ...(2)(2) - (1) : a = 3
代入(1) 得 b = - 1故 x^4 + 2x^3 + 5x + 2 =
(x^2 + 3x + 1) (x^2 - x + 2) = 0(x^2 + 3x + 1) = 0 或 (x^2 - x + 2) = 0x = (- 3 ± √5)/2 或 無實根