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受欢迎的代数 >

24x^5+10x^4-x^3-19x^2-5x+6=0

解答

24 x^{5} + 10 x^{4} - x^{3} - 19 x^{2} - 5 x + 6 = 0

解答

x = \frac{1}{2}, x = - \frac{2}{3}, x = \frac{3}{4}, x = - \frac{1}{2} + i \frac{3}{2}, x = - \frac{1}{2} - i \frac{3}{2}

求解步骤

24 x^{5} + 10 x^{4} - x^{3} - 19 x^{2} - 5 x + 6 = 0

因式分解

24 x^{5} + 10 x^{4} - x^{3} - 19 x^{2} - 5 x + 6 : (2 x - 1) (3 x + 2) (4 x - 3) (x^{2} + x + 1)

(2 x - 1) (3 x + 2) (4 x - 3) (x^{2} + x + 1) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

2 x - 1 = 0 or 3 x + 2 = 0 or 4 x - 3 = 0 or x^{2} + x + 1 = 0

解

2 x - 1 = 0 : x = \frac{1}{2}

解

3 x + 2 = 0 : x = - \frac{2}{3}

解

4 x - 3 = 0 : x = \frac{3}{4}

解

x^{2} + x + 1 = 0 : x = - \frac{1}{2} + i \frac{3}{2}, x = - \frac{1}{2} - i \frac{3}{2}

解为

x = \frac{1}{2}, x = - \frac{2}{3}, x = \frac{3}{4}, x = - \frac{1}{2} + i \frac{3}{2}, x = - \frac{1}{2} - i \frac{3}{2}

作图

流行的例子

根 4x^4-25x^2+36=0

roo t s 4 x^{4} - 25 x^{2} + 36 = 0

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

因式分解 x^4-13x^2+36=0

f a c t or x^{4} - 13 x^{2} + 36 = 0

x^{3} - 9 x - 12 = 0

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

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