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

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

Find the zeros of 4x^4-4x=0

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

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4 x^{4} - 4 x = 0

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

Solution steps

4 x^{4} - 4 x = 0

Factor

4 x^{4} - 4 x : 4 x (x^{3} - 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{3} - 1 = 0

Solve

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

The solutions are

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

4 x - 7 x^{5} + 16 x^{2} = 0

x, 4 x^{3} - 2 x = 0

y, 8 y - 8 x^{3} = 0

x^{3} - 6 x^{2} + 9 x - 8 = 0

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

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