What are the solutions to the equation x^4-1/8 x=0 ?

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

Find the zeros of x^4-1/8 x=0

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

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x^{4} - \frac{1}{8} x = 0

x = 0, x = \frac{1}{2}, x = - \frac{1}{4} + \frac{3}{4} i, x = - \frac{1}{4} - \frac{3}{4} i

Solution steps

x^{4} - \frac{1}{8} x = 0

Factor

x^{4} - \frac{1}{8} x : x (x^{3} - \frac{1}{8})

x (x^{3} - \frac{1}{8}) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{3} - \frac{1}{8} = 0

Solve

x^{3} - \frac{1}{8} = 0 : x = \frac{1}{2}, x = - \frac{1}{4} + \frac{3}{4} i, x = - \frac{1}{4} - \frac{3}{4} i

The solutions are

x = 0, x = \frac{1}{2}, x = - \frac{1}{4} + \frac{3}{4} i, x = - \frac{1}{4} - \frac{3}{4} i

2 x^{3} = 6

x^{3} + 2 x^{2} = 81 x + 162

6 t^{3} - 4 t^{2} = 16 t

3 x^{3} + x^{2} + 12 x + 4 = 0

m^{3} = - 1000

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