What are the solutions to the equation x^4=1000x ?

The solutions to the equation x^4=1000x are x=0,x=10,x=-5+5sqrt(3)i,x=-5-5sqrt(3)i

Find the zeros of x^4=1000x

The zeros of x^4=1000x are x=0,x=10,x=-5+5sqrt(3)i,x=-5-5sqrt(3)i

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x^{4} = 1000 x

x = 0, x = 10, x = - 5 + 53 i, x = - 5 - 53 i

Solution steps

x^{4} = 1000 x

Move

1000 x

to the left side

x^{4} - 1000 x = 0

Factor

x^{4} - 1000 x : x (x^{3} - 1000)

x (x^{3} - 1000) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{3} - 1000 = 0

Solve

x^{3} - 1000 = 0 : x = 10, x = - 5 + 53 i, x = - 5 - 53 i

The solutions are

x = 0, x = 10, x = - 5 + 53 i, x = - 5 - 53 i

x^{3} - 4 x = 2 x

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

z, z^{4} - 9 = 0

- (x - 1)^{3} = 8

- (x - 1)^{3} = 0

What are the solutions to the equation x^4=1000x ?
The solutions to the equation x^4=1000x are x=0,x=10,x=-5+5sqrt(3)i,x=-5-5sqrt(3)i
Find the zeros of x^4=1000x
The zeros of x^4=1000x are x=0,x=10,x=-5+5sqrt(3)i,x=-5-5sqrt(3)i