What are the solutions to the equation x^4+13x^2+40=0 ?

The solutions to the equation x^4+13x^2+40=0 are x=sqrt(5)i,x=-sqrt(5)i,x=2sqrt(2)i,x=-2sqrt(2)i

Find the zeros of x^4+13x^2+40=0

The zeros of x^4+13x^2+40=0 are x=sqrt(5)i,x=-sqrt(5)i,x=2sqrt(2)i,x=-2sqrt(2)i

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x^{4} + 13 x^{2} + 40 = 0

x = 5 i, x = - 5 i, x = 22 i, x = - 22 i

Solution steps

x^{4} + 13 x^{2} + 40 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

u^{2} + 13 u + 40 = 0

Solve

u^{2} + 13 u + 40 = 0 : u = - 5, u = - 8

u = - 5, u = - 8

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = - 5 : x = 5 i, x = - 5 i

Solve

x^{2} = - 8 : x = 22 i, x = - 22 i

The solutions are

x = 5 i, x = - 5 i, x = 22 i, x = - 22 i

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

- x^{3} + 6 x^{2} + 15 x + 8

a^{3} + 5 a + 6 = 0

x^{5} - 243 = 0

x^{3} - 13 x^{2} + 23 x - 11 = 0

What are the solutions to the equation x^4+13x^2+40=0 ?
The solutions to the equation x^4+13x^2+40=0 are x=sqrt(5)i,x=-sqrt(5)i,x=2sqrt(2)i,x=-2sqrt(2)i
Find the zeros of x^4+13x^2+40=0
The zeros of x^4+13x^2+40=0 are x=sqrt(5)i,x=-sqrt(5)i,x=2sqrt(2)i,x=-2sqrt(2)i