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受欢迎的代数 >

r^5-3r^4+3r^3-3r^2+2r=0

解答

r^{5} - 3 r^{4} + 3 r^{3} - 3 r^{2} + 2 r = 0

解答

r = 0, r = 1, r = 2, r = i, r = - i

求解步骤

r^{5} - 3 r^{4} + 3 r^{3} - 3 r^{2} + 2 r = 0

因式分解

r^{5} - 3 r^{4} + 3 r^{3} - 3 r^{2} + 2 r : r (r - 1) (r - 2) (r^{2} + 1)

r (r - 1) (r - 2) (r^{2} + 1) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

r = 0 or r - 1 = 0 or r - 2 = 0 or r^{2} + 1 = 0

解

r - 1 = 0 : r = 1

解

r - 2 = 0 : r = 2

解

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

解为

r = 0, r = 1, r = 2, r = i, r = - i

作图

流行的例子

根 x^3-2x^2-11x+12

roo t s x^{3} - 2 x^{2} - 11 x + 12

x^4+9x^3+12x^2-34x+12=0

x^{4} + 9 x^{3} + 12 x^{2} - 34 x + 12 = 0

r^4-2r^3+r^2+2r-2=0

r^{4} - 2 r^{3} + r^{2} + 2 r - 2 = 0

3 x^{3} - 81 = 0

x^3-594x+3186=0

x^{3} - 594 x + 3186 = 0