What are the solutions to the equation 3x^4=1536x ?

The solutions to the equation 3x^4=1536x are x=0,x=8,x=-4+4sqrt(3)i,x=-4-4sqrt(3)i

Find the zeros of 3x^4=1536x

The zeros of 3x^4=1536x are x=0,x=8,x=-4+4sqrt(3)i,x=-4-4sqrt(3)i

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3 x^{4} = 1536 x

x = 0, x = 8, x = - 4 + 43 i, x = - 4 - 43 i

Solution steps

3 x^{4} = 1536 x

Move

1536 x

to the left side

3 x^{4} - 1536 x = 0

Factor

3 x^{4} - 1536 x : 3 x (x - 8) (x^{2} + 8 x + 64)

3 x (x - 8) (x^{2} + 8 x + 64) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - 8 = 0 or x^{2} + 8 x + 64 = 0

Solve

x - 8 = 0 : x = 8

Solve

x^{2} + 8 x + 64 = 0 : x = - 4 + 43 i, x = - 4 - 43 i

The solutions are

x = 0, x = 8, x = - 4 + 43 i, x = - 4 - 43 i

16 x^{3} + 64 x^{2} - x - 4 = 0

6 x^{4} - 5 x^{3} - 38 x^{2} - 5 x + 6 = 0

6 x^{4} - x^{3} + 5 x^{2} - x - 1 = 0

y, x = y^{3} + 1

2 x^{4} - 3 x^{2} - 20 = 0

What are the solutions to the equation 3x^4=1536x ?
The solutions to the equation 3x^4=1536x are x=0,x=8,x=-4+4sqrt(3)i,x=-4-4sqrt(3)i
Find the zeros of 3x^4=1536x
The zeros of 3x^4=1536x are x=0,x=8,x=-4+4sqrt(3)i,x=-4-4sqrt(3)i