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受欢迎的代数 >

0=3x^4-8x^3+6x^2

解答

0 = 3 x^{4} - 8 x^{3} + 6 x^{2}

解答

x = 0, x = \frac{4}{3} + i \frac{2}{3}, x = \frac{4}{3} - i \frac{2}{3}

求解步骤

0 = 3 x^{4} - 8 x^{3} + 6 x^{2}

交换两边

3 x^{4} - 8 x^{3} + 6 x^{2} = 0

因式分解

3 x^{4} - 8 x^{3} + 6 x^{2} : x^{2} (3 x^{2} - 8 x + 6)

x^{2} (3 x^{2} - 8 x + 6) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x = 0 or 3 x^{2} - 8 x + 6 = 0

解

3 x^{2} - 8 x + 6 = 0 : x = \frac{4}{3} + i \frac{2}{3}, x = \frac{4}{3} - i \frac{2}{3}

解为

x = 0, x = \frac{4}{3} + i \frac{2}{3}, x = \frac{4}{3} - i \frac{2}{3}

作图

流行的例子

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

3=0.03x^3+0.05x^2

3 = 0.03 x^{3} + 0.05 x^{2}

-12x^5-6x^3+10=0

- 12 x^{5} - 6 x^{3} + 10 = 0

3x^3-33x^2+30x=0

3 x^{3} - 33 x^{2} + 30 x = 0

3t^4-4t^3-12t^2+6=0

3 t^{4} - 4 t^{3} - 12 t^{2} + 6 = 0