What are the solutions to the equation 2x^5=16x^2 ?

The solutions to the equation 2x^5=16x^2 are x=0,x=2,x=-1+sqrt(3)i,x=-1-sqrt(3)i

Find the zeros of 2x^5=16x^2

The zeros of 2x^5=16x^2 are x=0,x=2,x=-1+sqrt(3)i,x=-1-sqrt(3)i

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2 x^{5} = 16 x^{2}

x = 0, x = 2, x = - 1 + 3 i, x = - 1 - 3 i

Solution steps

2 x^{5} = 16 x^{2}

Move

16 x^{2}

to the left side

2 x^{5} - 16 x^{2} = 0

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 2 = 0 : x = 2

Solve

x^{2} + 2 x + 4 = 0 : x = - 1 + 3 i, x = - 1 - 3 i

The solutions are

x = 0, x = 2, x = - 1 + 3 i, x = - 1 - 3 i

x^{4} + 9 x^{3} + x^{2} + 9 x = 0

x^{3} + x^{2} + 2 x + 3 = 0

(r^{2} + 5 r) (r^{2} + 5 r + 3) = 4

x^{4} + 2 x^{3} + x^{2} = 0

- 3 x^{4} + 25 = - 5 + x^{6}

What are the solutions to the equation 2x^5=16x^2 ?
The solutions to the equation 2x^5=16x^2 are x=0,x=2,x=-1+sqrt(3)i,x=-1-sqrt(3)i
Find the zeros of 2x^5=16x^2
The zeros of 2x^5=16x^2 are x=0,x=2,x=-1+sqrt(3)i,x=-1-sqrt(3)i