What are the solutions to the equation x^4+4x^2-117=0 ?

The solutions to the equation x^4+4x^2-117=0 are x=3,x=-3,x=sqrt(13)i,x=-sqrt(13)i

Find the zeros of x^4+4x^2-117=0

The zeros of x^4+4x^2-117=0 are x=3,x=-3,x=sqrt(13)i,x=-sqrt(13)i

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x^{4} + 4 x^{2} - 117 = 0

x = 3, x = - 3, x = 13 i, x = - 13 i

Solution steps

x^{4} + 4 x^{2} - 117 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

u^{2} + 4 u - 117 = 0

Solve

u^{2} + 4 u - 117 = 0 : u = 9, u = - 13

u = 9, u = - 13

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = 9 : x = 3, x = - 3

Solve

x^{2} = - 13 : x = 13 i, x = - 13 i

The solutions are

x = 3, x = - 3, x = 13 i, x = - 13 i

t^{3} + 4 t^{2} - 44 t - 96 = 0

3 (x^{3} - x) = 0

4 x^{4} - 25 x^{2} + 36 = 0

x^{3} - 2 x + 2

x^{4} - 13 x^{2} + 36 = 0

What are the solutions to the equation x^4+4x^2-117=0 ?
The solutions to the equation x^4+4x^2-117=0 are x=3,x=-3,x=sqrt(13)i,x=-sqrt(13)i
Find the zeros of x^4+4x^2-117=0
The zeros of x^4+4x^2-117=0 are x=3,x=-3,x=sqrt(13)i,x=-sqrt(13)i