What are the solutions to the equation -4x^5=256x^2 ?

The solutions to the equation -4x^5=256x^2 are x=0,x=-4,x=2+2sqrt(3)i,x=2-2sqrt(3)i

Find the zeros of -4x^5=256x^2

The zeros of -4x^5=256x^2 are x=0,x=-4,x=2+2sqrt(3)i,x=2-2sqrt(3)i

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- 4 x^{5} = 256 x^{2}

x = 0, x = - 4, x = 2 + 23 i, x = 2 - 23 i

Solution steps

- 4 x^{5} = 256 x^{2}

Move

256 x^{2}

to the left side

- 4 x^{5} - 256 x^{2} = 0

Factor

- 4 x^{5} - 256 x^{2} : - 4 x^{2} (x + 4) (x^{2} - 4 x + 16)

- 4 x^{2} (x + 4) (x^{2} - 4 x + 16) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x + 4 = 0 or x^{2} - 4 x + 16 = 0

Solve

x + 4 = 0 : x = - 4

Solve

x^{2} - 4 x + 16 = 0 : x = 2 + 23 i, x = 2 - 23 i

The solutions are

x = 0, x = - 4, x = 2 + 23 i, x = 2 - 23 i

8 = a^{3}

0 = 2 x^{3} + 8 x^{2} + 14 x + 24

- 2 x^{5} + 7 x^{2} - 3 = 0

5 = 2 x^{3} - 3.2

3 x^{4} + 15 x^{2} - 72 = 0

What are the solutions to the equation -4x^5=256x^2 ?
The solutions to the equation -4x^5=256x^2 are x=0,x=-4,x=2+2sqrt(3)i,x=2-2sqrt(3)i
Find the zeros of -4x^5=256x^2
The zeros of -4x^5=256x^2 are x=0,x=-4,x=2+2sqrt(3)i,x=2-2sqrt(3)i