What are the solutions to the equation 6x^4=3072x ?

The solutions to the equation 6x^4=3072x are x=0,x=8,x=-4+4sqrt(3)i,x=-4-4sqrt(3)i

Find the zeros of 6x^4=3072x

The zeros of 6x^4=3072x are x=0,x=8,x=-4+4sqrt(3)i,x=-4-4sqrt(3)i

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6 x^{4} = 3072 x

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

Solution steps

6 x^{4} = 3072 x

Move

3072 x

to the left side

6 x^{4} - 3072 x = 0

Factor

6 x^{4} - 3072 x : 6 x (x - 8) (x^{2} + 8 x + 64)

6 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

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

z^{7} = - 1 + 2 j

x^{4} + x^{2} + 17 = 0

4 X^{3} - 24 X^{2} = 0

x^{4} - 2 x^{3} + 21 x^{2} - 32 x + 80 = 0

What are the solutions to the equation 6x^4=3072x ?
The solutions to the equation 6x^4=3072x are x=0,x=8,x=-4+4sqrt(3)i,x=-4-4sqrt(3)i
Find the zeros of 6x^4=3072x
The zeros of 6x^4=3072x are x=0,x=8,x=-4+4sqrt(3)i,x=-4-4sqrt(3)i