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受欢迎的代数 >

0=x^2-2x^3-10x+11

解答

0 = x^{2} - 2 x^{3} - 10 x + 11

解答

x = 1, x = - \frac{1}{4} + i \frac{87}{4}, x = - \frac{1}{4} - i \frac{87}{4}

求解步骤

0 = x^{2} - 2 x^{3} - 10 x + 11

交换两边

x^{2} - 2 x^{3} - 10 x + 11 = 0

改写成标准形式

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

- 2 x^{3} + x^{2} - 10 x + 11 = 0

因式分解

- 2 x^{3} + x^{2} - 10 x + 11 : - (x - 1) (2 x^{2} + x + 11)

- (x - 1) (2 x^{2} + x + 11) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x - 1 = 0 or 2 x^{2} + x + 11 = 0

解

x - 1 = 0 : x = 1

解

2 x^{2} + x + 11 = 0 : x = - \frac{1}{4} + i \frac{87}{4}, x = - \frac{1}{4} - i \frac{87}{4}

解为

x = 1, x = - \frac{1}{4} + i \frac{87}{4}, x = - \frac{1}{4} - i \frac{87}{4}

作图

流行的例子

3x^4+5x^3-11x^2+2x-3=0

3 x^{4} + 5 x^{3} - 11 x^{2} + 2 x - 3 = 0

x^2(x^2-81)-49(x^2-81)=0

x^{2} (x^{2} - 81) - 49 (x^{2} - 81) = 0

3 x^{3} - 5 x^{2} - 1 = 0

(x + 2)^{4} = 81

5=4x^3+12x^2+12x+4

5 = 4 x^{3} + 12 x^{2} + 12 x + 4