What are the solutions to the equation x^4+4x^2-21=0 ?

The solutions to the equation x^4+4x^2-21=0 are x=sqrt(3),x=-sqrt(3),x=sqrt(7)i,x=-sqrt(7)i

Find the zeros of x^4+4x^2-21=0

The zeros of x^4+4x^2-21=0 are x=sqrt(3),x=-sqrt(3),x=sqrt(7)i,x=-sqrt(7)i

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x^{4} + 4 x^{2} - 21 = 0

x = 3, x = - 3, x = 7 i, x = - 7 i

Solution steps

x^{4} + 4 x^{2} - 21 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

u^{2} + 4 u - 21 = 0

Solve

u^{2} + 4 u - 21 = 0 : u = 3, u = - 7

u = 3, u = - 7

Substitute back

u = x^{2},

solve for

x

Solve

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

Solve

x^{2} = - 7 : x = 7 i, x = - 7 i

The solutions are

x = 3, x = - 3, x = 7 i, x = - 7 i

y, x^{2} + y^{2} = (2 x^{2} + 2 y^{2} - x)^{2}

x^{3}

x^{3} + 4 x^{2} = 9 x + 36

x^{3} + 2 x^{2} - 19 x - 20

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

What are the solutions to the equation x^4+4x^2-21=0 ?
The solutions to the equation x^4+4x^2-21=0 are x=sqrt(3),x=-sqrt(3),x=sqrt(7)i,x=-sqrt(7)i
Find the zeros of x^4+4x^2-21=0
The zeros of x^4+4x^2-21=0 are x=sqrt(3),x=-sqrt(3),x=sqrt(7)i,x=-sqrt(7)i