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受欢迎的代数 >

根 x^4-4x^3+8x^2-16x+16

解答

根

x^{4} - 4 x^{3} + 8 x^{2} - 16 x + 16

解答

x = 2, x = 2 i, x = - 2 i

求解步骤

x^{4} - 4 x^{3} + 8 x^{2} - 16 x + 16

根与 X 轴相交

(y = 0)

x^{4} - 4 x^{3} + 8 x^{2} - 16 x + 16 = 0

因式分解

x^{4} - 4 x^{3} + 8 x^{2} - 16 x + 16 : (x - 2)^{2} (x^{2} + 4)

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

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

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

解

x - 2 = 0 : x = 2

解

x^{2} + 4 = 0 : x = 2 i, x = - 2 i

解为

x = 2, x = 2 i, x = - 2 i

作图

流行的例子

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2 x^{3} - 3 x^{2} - 32 x + 48 = 0

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