What are the solutions to the equation roots x^4+6x^2+8 ?

The solutions to the equation roots x^4+6x^2+8 are x=sqrt(2)i,x=-sqrt(2)i,x=2i,x=-2i

Find the zeros of roots x^4+6x^2+8

The zeros of roots x^4+6x^2+8 are x=sqrt(2)i,x=-sqrt(2)i,x=2i,x=-2i

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roots

x^{4} + 6 x^{2} + 8

x = 2 i, x = - 2 i, x = 2 i, x = - 2 i

Solution steps

x^{4} + 6 x^{2} + 8

The roots are the intercepts with the x-axis

(y = 0)

x^{4} + 6 x^{2} + 8 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

u^{2} + 6 u + 8 = 0

Solve

u^{2} + 6 u + 8 = 0 : u = - 2, u = - 4

u = - 2, u = - 4

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = - 2 : x = 2 i, x = - 2 i

Solve

x^{2} = - 4 : x = 2 i, x = - 2 i

The solutions are

x = 2 i, x = - 2 i, x = 2 i, x = - 2 i

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

x^{3} + 3 x^{2} + 2 x

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

x^{8} - 256 = 0

(x + 2)^{4} - 4 (x + 2)^{2} - 5 = 0

What are the solutions to the equation roots x^4+6x^2+8 ?
The solutions to the equation roots x^4+6x^2+8 are x=sqrt(2)i,x=-sqrt(2)i,x=2i,x=-2i
Find the zeros of roots x^4+6x^2+8
The zeros of roots x^4+6x^2+8 are x=sqrt(2)i,x=-sqrt(2)i,x=2i,x=-2i