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受欢迎的代数 >

x^3+2x^2-5x+12=0

解答

x^{3} + 2 x^{2} - 5 x + 12 = 0

解答

x = - 4, x = 1 + 2 i, x = 1 - 2 i

求解步骤

x^{3} + 2 x^{2} - 5 x + 12 = 0

因式分解

x^{3} + 2 x^{2} - 5 x + 12 : (x + 4) (x^{2} - 2 x + 3)

(x + 4) (x^{2} - 2 x + 3) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x + 4 = 0 or x^{2} - 2 x + 3 = 0

解

x + 4 = 0 : x = - 4

解

x^{2} - 2 x + 3 = 0 : x = 1 + 2 i, x = 1 - 2 i

解为

x = - 4, x = 1 + 2 i, x = 1 - 2 i

作图

流行的例子

x^6-4x^4-16x^2+64=0

x^{6} - 4 x^{4} - 16 x^{2} + 64 = 0

x^{3} - x^{2} - 2 x + 2 = 0

x^{3} - x^{2} - 2 x + 1 = 0

15x^5-20x^4=6x^3-8x^2

15 x^{5} - 20 x^{4} = 6 x^{3} - 8 x^{2}

5 x^{4} + 12 = x - 12