What are the solutions to the equation x^4=8x ?

The solutions to the equation x^4=8x are x=0,x=2,x=-1+sqrt(3)i,x=-1-sqrt(3)i

Find the zeros of x^4=8x

The zeros of x^4=8x are x=0,x=2,x=-1+sqrt(3)i,x=-1-sqrt(3)i

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x^{4} = 8 x

x = 0, x = 2, x = - 1 + 3 i, x = - 1 - 3 i

Solution steps

x^{4} = 8 x

Move

8 x

to the left side

x^{4} - 8 x = 0

Factor

x^{4} - 8 x : x (x^{3} - 8)

x (x^{3} - 8) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{3} - 8 = 0

Solve

x^{3} - 8 = 0 : x = 2, x = - 1 + 3 i, x = - 1 - 3 i

The solutions are

x = 0, x = 2, x = - 1 + 3 i, x = - 1 - 3 i

x^{3} + 5 x^{2} - 20 = 0

18 x^{3} + 9 x^{2} - 2 x - 1 = 0

4 x^{3} - 1 = 2 x^{2} - 2 x

x^{3} + 4 x - 4 = 0

x (x + 4) (x - 1) = 0

What are the solutions to the equation x^4=8x ?
The solutions to the equation x^4=8x are x=0,x=2,x=-1+sqrt(3)i,x=-1-sqrt(3)i
Find the zeros of x^4=8x
The zeros of x^4=8x are x=0,x=2,x=-1+sqrt(3)i,x=-1-sqrt(3)i