What are the solutions to the equation roots x^4+3x^2-4 ?

The solutions to the equation roots x^4+3x^2-4 are x=1,x=-1,x=2i,x=-2i

Find the zeros of roots x^4+3x^2-4

The zeros of roots x^4+3x^2-4 are x=1,x=-1,x=2i,x=-2i

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roots

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

x = 1, x = - 1, x = 2 i, x = - 2 i

Solution steps

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

The roots are the intercepts with the x-axis

(y = 0)

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

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

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

Solve

u^{2} + 3 u - 4 = 0 : u = 1, u = - 4

u = 1, u = - 4

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = 1 : x = 1, x = - 1

Solve

x^{2} = - 4 : x = 2 i, x = - 2 i

The solutions are

x = 1, x = - 1, x = 2 i, x = - 2 i

2 x^{4} = 50

x^{4} - 4 x^{3} + 5 x^{2} - 4 x + 4 = 0

(x - 5) (x^{2} + 4 x + 4) = 8 (x + 2)

3 x^{3} - 19 x^{2} + 33 x - 9 = 0

6 x^{3} + 25 x^{2} - 24 x + 5

What are the solutions to the equation roots x^4+3x^2-4 ?
The solutions to the equation roots x^4+3x^2-4 are x=1,x=-1,x=2i,x=-2i
Find the zeros of roots x^4+3x^2-4
The zeros of roots x^4+3x^2-4 are x=1,x=-1,x=2i,x=-2i