What are the solutions to the equation x^4+8x^2+12=0 ?

The solutions to the equation x^4+8x^2+12=0 are x=sqrt(2)i,x=-sqrt(2)i,x=sqrt(6)i,x=-sqrt(6)i

Find the zeros of x^4+8x^2+12=0

The zeros of x^4+8x^2+12=0 are x=sqrt(2)i,x=-sqrt(2)i,x=sqrt(6)i,x=-sqrt(6)i

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x^{4} + 8 x^{2} + 12 = 0

x = 2 i, x = - 2 i, x = 6 i, x = - 6 i

Solution steps

x^{4} + 8 x^{2} + 12 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

u^{2} + 8 u + 12 = 0

Solve

u^{2} + 8 u + 12 = 0 : u = - 2, u = - 6

u = - 2, u = - 6

Substitute back

u = x^{2},

solve for

x

Solve

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

Solve

x^{2} = - 6 : x = 6 i, x = - 6 i

The solutions are

x = 2 i, x = - 2 i, x = 6 i, x = - 6 i

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

4 x^{3} - 6 x^{2} + 4 x = 0

x^{4} + 2 x^{3} + x^{2} + 8 x - 12

y, x^{5} + y^{5} = 16

x^{4} + 4 x^{3} + 9 x^{2} + 10 x + 7 = 0

What are the solutions to the equation x^4+8x^2+12=0 ?
The solutions to the equation x^4+8x^2+12=0 are x=sqrt(2)i,x=-sqrt(2)i,x=sqrt(6)i,x=-sqrt(6)i
Find the zeros of x^4+8x^2+12=0
The zeros of x^4+8x^2+12=0 are x=sqrt(2)i,x=-sqrt(2)i,x=sqrt(6)i,x=-sqrt(6)i