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受欢迎的代数 >

f^4-4f^3-25f=0

解答

f^{4} - 4 f^{3} - 25 f = 0

解答

f = 0, f = 5, f = - \frac{1}{2} + i \frac{19}{2}, f = - \frac{1}{2} - i \frac{19}{2}

求解步骤

f^{4} - 4 f^{3} - 25 f = 0

因式分解

f^{4} - 4 f^{3} - 25 f : f (f - 5) (f^{2} + f + 5)

f (f - 5) (f^{2} + f + 5) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

f = 0 or f - 5 = 0 or f^{2} + f + 5 = 0

解

f - 5 = 0 : f = 5

解

f^{2} + f + 5 = 0 : f = - \frac{1}{2} + i \frac{19}{2}, f = - \frac{1}{2} - i \frac{19}{2}

解为

f = 0, f = 5, f = - \frac{1}{2} + i \frac{19}{2}, f = - \frac{1}{2} - i \frac{19}{2}

作图

流行的例子

-16x^3-16x^2+60x=0

- 16 x^{3} - 16 x^{2} + 60 x = 0

solvefor y,x=y^3-2

so l v e f or y, x = y^{3} - 2

12 = 305 \cdot x^{3}

solvefor x,x^3-2x^2-9x=18

so l v e f or x, x^{3} - 2 x^{2} - 9 x = 18

x = (3 x^{2} + 2)^{2}