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受欢迎的代数 >

x^4-128x^2-8192x-61440=0

解答

x^{4} - 128 \cdot x^{2} - 8192 \cdot x - 61440 = 0

解答

x = - 8, x = 24, x = - 8 + 16 i, x = - 8 - 16 i

求解步骤

x^{4} - 128 x^{2} - 8192 x - 61440 = 0

因式分解

x^{4} - 128 x^{2} - 8192 x - 61440 : (x + 8) (x - 24) (x^{2} + 16 x + 320)

(x + 8) (x - 24) (x^{2} + 16 x + 320) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x + 8 = 0 or x - 24 = 0 or x^{2} + 16 x + 320 = 0

解

x + 8 = 0 : x = - 8

解

x - 24 = 0 : x = 24

解

x^{2} + 16 x + 320 = 0 : x = - 8 + 16 i, x = - 8 - 16 i

解为

x = - 8, x = 24, x = - 8 + 16 i, x = - 8 - 16 i

作图

流行的例子

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