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受欢迎的代数 >

20x^4-5x^3-12x^2+3x=0

解答

20 x^{4} - 5 x^{3} - 12 x^{2} + 3 x = 0

解答

x = 0, x = \frac{1}{4}, x = - \frac{3}{5}, x = \frac{3}{5}

+1

十进制

x = 0, x = 0.25, x = - 0.77459 \dots, x = 0.77459 \dots

求解步骤

20 x^{4} - 5 x^{3} - 12 x^{2} + 3 x = 0

因式分解

20 x^{4} - 5 x^{3} - 12 x^{2} + 3 x : x (4 x - 1) (5 x + 3) (5 x - 3)

x (4 x - 1) (5 x + 3) (5 x - 3) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x = 0 or 4 x - 1 = 0 or 5 x + 3 = 0 or 5 x - 3 = 0

解

4 x - 1 = 0 : x = \frac{1}{4}

解

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

解

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

解为

x = 0, x = \frac{1}{4}, x = - \frac{3}{5}, x = \frac{3}{5}

作图

流行的例子

2x^3+2x^2-8x+12=0

2 x^{3} + 2 x^{2} - 8 x + 12 = 0

x^{4} + 16 = 0

n^3-3n^2+2n-336=0

n^{3} - 3 n^{2} + 2 n - 336 = 0

solvefor x,x^3-y^3+z^3=4

so l v e f or x, x^{3} - y^{3} + z^{3} = 4

m^4+2m^3+3m^2+2m+1=0

m^{4} + 2 m^{3} + 3 m^{2} + 2 m + 1 = 0