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受欢迎的代数 >

2m^5-7m^4+12m^3+8m^2=0

解答

2 m^{5} - 7 m^{4} + 12 m^{3} + 8 m^{2} = 0

解答

m = 0, m = - \frac{1}{2}, m = 2 + 2 i, m = 2 - 2 i

求解步骤

2 m^{5} - 7 m^{4} + 12 m^{3} + 8 m^{2} = 0

因式分解

2 m^{5} - 7 m^{4} + 12 m^{3} + 8 m^{2} : m^{2} (2 m + 1) (m^{2} - 4 m + 8)

m^{2} (2 m + 1) (m^{2} - 4 m + 8) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

m = 0 or 2 m + 1 = 0 or m^{2} - 4 m + 8 = 0

解

2 m + 1 = 0 : m = - \frac{1}{2}

解

m^{2} - 4 m + 8 = 0 : m = 2 + 2 i, m = 2 - 2 i

解为

m = 0, m = - \frac{1}{2}, m = 2 + 2 i, m = 2 - 2 i

作图

流行的例子

m^5-4m^4+4m^3=0

m^{5} - 4 m^{4} + 4 m^{3} = 0

3x^6-39x^4+108x^2=0

3 x^{6} - 39 x^{4} + 108 x^{2} = 0

16 x^{4} - 625 = 0

x^{5} + 3 x^{3} - 4 x = 0

r^3-7r^2+16r-12=0

r^{3} - 7 r^{2} + 16 r - 12 = 0