What are the solutions to the equation 3x^4-3x=0 ?

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

Find the zeros of 3x^4-3x=0

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

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3 x^{4} - 3 x = 0

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

Solution steps

3 x^{4} - 3 x = 0

Factor

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

3 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

25 x^{4} + 4 = 29 x^{2}

8 x^{3} + 3 x^{2} - 16 x - 1 = 0

x = x^{5}

n^{3} - n^{2} - 16 n - 20 = 0

x^{3} - 8 x^{2} - 15 = 0

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