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受欢迎的代数 >

根 5x^3-3x^2+180x-108

解答

根

5 x^{3} - 3 x^{2} + 180 x - 108

解答

x = \frac{3}{5}, x = 6 i, x = - 6 i

求解步骤

5 x^{3} - 3 x^{2} + 180 x - 108

根与 X 轴相交

(y = 0)

5 x^{3} - 3 x^{2} + 180 x - 108 = 0

因式分解

5 x^{3} - 3 x^{2} + 180 x - 108 : (5 x - 3) (x^{2} + 36)

(5 x - 3) (x^{2} + 36) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

5 x - 3 = 0 or x^{2} + 36 = 0

解

5 x - 3 = 0 : x = \frac{3}{5}

解

x^{2} + 36 = 0 : x = 6 i, x = - 6 i

解为

x = \frac{3}{5}, x = 6 i, x = - 6 i

作图

流行的例子

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

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

6 x^{3} - 5 x - 1 = 0

x^4-5x^3+6x^2+4x-8=0

x^{4} - 5 x^{3} + 6 x^{2} + 4 x - 8 = 0

8x^4+10x^2-12=0

8 x^{4} + 10 x^{2} - 12 = 0

w^{3} = 27