What are the solutions to the equation x^4+15x^2+54=0 ?

The solutions to the equation x^4+15x^2+54=0 are x=sqrt(6)i,x=-sqrt(6)i,x=3i,x=-3i

Find the zeros of x^4+15x^2+54=0

The zeros of x^4+15x^2+54=0 are x=sqrt(6)i,x=-sqrt(6)i,x=3i,x=-3i

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x^{4} + 15 x^{2} + 54 = 0

x = 6 i, x = - 6 i, x = 3 i, x = - 3 i

Solution steps

x^{4} + 15 x^{2} + 54 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

u^{2} + 15 u + 54 = 0

Solve

u^{2} + 15 u + 54 = 0 : u = - 6, u = - 9

u = - 6, u = - 9

Substitute back

u = x^{2},

solve for

x

Solve

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

Solve

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

The solutions are

x = 6 i, x = - 6 i, x = 3 i, x = - 3 i

4 x^{4} - 28 x^{3} + 61 x^{2} - 42 x + 9 = 0

16 x^{4} - 52 x^{2} + 36 = 0

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

x^{5} = 18 x^{3} - 81 x

m^{5} + 5 m^{4} - 2 m^{3} - 10 m^{2} + m + 5 = 0

What are the solutions to the equation x^4+15x^2+54=0 ?
The solutions to the equation x^4+15x^2+54=0 are x=sqrt(6)i,x=-sqrt(6)i,x=3i,x=-3i
Find the zeros of x^4+15x^2+54=0
The zeros of x^4+15x^2+54=0 are x=sqrt(6)i,x=-sqrt(6)i,x=3i,x=-3i