What are the solutions to the equation f^4-4f^3=25f ?

The solutions to the equation f^4-4f^3=25f are f=0,f=5,f=-1/2+i(sqrt(19))/2 ,f=-1/2-i(sqrt(19))/2

Find the zeros of f^4-4f^3=25f

The zeros of f^4-4f^3=25f are f=0,f=5,f=-1/2+i(sqrt(19))/2 ,f=-1/2-i(sqrt(19))/2

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

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

Solution steps

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

Move

25 f

to the left side

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

f - 5 = 0 : f = 5

Solve

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

The solutions are

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

x^{4} - 5 x^{3} - 7 x^{2} + 29 x = - 30

n^{3} = 2 n

x^{3} + 2 x = 400

11000 = 3000 (1 + x)^{5}

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

What are the solutions to the equation f^4-4f^3=25f ?
The solutions to the equation f^4-4f^3=25f are f=0,f=5,f=-1/2+i(sqrt(19))/2 ,f=-1/2-i(sqrt(19))/2
Find the zeros of f^4-4f^3=25f
The zeros of f^4-4f^3=25f are f=0,f=5,f=-1/2+i(sqrt(19))/2 ,f=-1/2-i(sqrt(19))/2