What are the solutions to the equation x^5+x^3+8x^2+8=0 ?

The solutions to the equation x^5+x^3+8x^2+8=0 are x=-2,x=i,x=-i,x=1+sqrt(3)i,x=1-sqrt(3)i

Find the zeros of x^5+x^3+8x^2+8=0

The zeros of x^5+x^3+8x^2+8=0 are x=-2,x=i,x=-i,x=1+sqrt(3)i,x=1-sqrt(3)i

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x^{5} + x^{3} + 8 x^{2} + 8 = 0

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

Solution steps

x^{5} + x^{3} + 8 x^{2} + 8 = 0

Factor

x^{5} + x^{3} + 8 x^{2} + 8 : (x + 2) (x^{2} + 1) (x^{2} - 2 x + 4)

(x + 2) (x^{2} + 1) (x^{2} - 2 x + 4) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 2 = 0 or x^{2} + 1 = 0 or x^{2} - 2 x + 4 = 0

Solve

x + 2 = 0 : x = - 2

Solve

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

Solve

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

The solutions are

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

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

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

- x^{3} - 6 x^{2} - 8 x = 0

\frac{7}{9} = a^{392}

x^{3} + 4 x^{2} + 5 x + 4 = 0

What are the solutions to the equation x^5+x^3+8x^2+8=0 ?
The solutions to the equation x^5+x^3+8x^2+8=0 are x=-2,x=i,x=-i,x=1+sqrt(3)i,x=1-sqrt(3)i
Find the zeros of x^5+x^3+8x^2+8=0
The zeros of x^5+x^3+8x^2+8=0 are x=-2,x=i,x=-i,x=1+sqrt(3)i,x=1-sqrt(3)i