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受欢迎的代数 >

4x^4+10x^3=6x^2+15x

解答

4 x^{4} + 10 x^{3} = 6 x^{2} + 15 x

解答

x = 0, x = - \frac{5}{2}, x = - \frac{3}{2}, x = \frac{3}{2}

+1

十进制

x = 0, x = - 2.5, x = - 1.22474 \dots, x = 1.22474 \dots

求解步骤

4 x^{4} + 10 x^{3} = 6 x^{2} + 15 x

将

15 x

para o lado esquerdo

4 x^{4} + 10 x^{3} - 15 x = 6 x^{2}

将

6 x^{2}

para o lado esquerdo

4 x^{4} + 10 x^{3} - 15 x - 6 x^{2} = 0

因式分解

4 x^{4} + 10 x^{3} - 15 x - 6 x^{2} : x (2 x + 5) (2 x + 3) (2 x - 3)

x (2 x + 5) (2 x + 3) (2 x - 3) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x = 0 or 2 x + 5 = 0 or 2 x + 3 = 0 or 2 x - 3 = 0

解

2 x + 5 = 0 : x = - \frac{5}{2}

解

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

解

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

解为

x = 0, x = - \frac{5}{2}, x = - \frac{3}{2}, x = \frac{3}{2}

作图

流行的例子

- x^{3} + 7 x + 6 = 0

-2x(3x+1)(x-8)(x+2)=0

- 2 x (3 x + 1) (x - 8) (x + 2) = 0

9x^4+27x^3-4x^2-12x=0

9 x^{4} + 27 x^{3} - 4 x^{2} - 12 x = 0

x^3-9x^2+27x-27=0

x^{3} - 9 x^{2} + 27 x - 27 = 0

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

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