solve x^4 - 2x^3 + 4x^2 + 30x - 13 = 0 given that 2+3i is a

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solve x^4 - 2x^3 + 4x^2 + 30x - 13 = 0 given that 2+3i is a root.

你好!
2+3i 是一个根,那么还有一个虚数根是 2-3i
（方程的虚数根总是一对共轭虚数）
这两个根对应的一元二次方程是 x² - 4x+13 = 0
于是原方程可以写成 (x² - 4x+13)(x²+px+q) = 0
显然 q= - 1 ,p - 4 = - 2 （x³的系数）
即 p=2,q= -1
解方程 x²+2x - 1 = 0得
x = -1 ±√2
于是原方程的根为：2±3i,-1±√2

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