What are the solutions to the equation x^4+5x^2-14=0 ?

The solutions to the equation x^4+5x^2-14=0 are x=sqrt(2),x=-sqrt(2),x=sqrt(7)i,x=-sqrt(7)i

Find the zeros of x^4+5x^2-14=0

The zeros of x^4+5x^2-14=0 are x=sqrt(2),x=-sqrt(2),x=sqrt(7)i,x=-sqrt(7)i

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x^{4} + 5 x^{2} - 14 = 0

x = 2, x = - 2, x = 7 i, x = - 7 i

Solution steps

x^{4} + 5 x^{2} - 14 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

u^{2} + 5 u - 14 = 0

Solve

u^{2} + 5 u - 14 = 0 : u = 2, u = - 7

u = 2, u = - 7

Substitute back

u = x^{2},

solve for

x

Solve

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

Solve

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

The solutions are

x = 2, x = - 2, x = 7 i, x = - 7 i

x, x^{3} - y = 2

x, x^{3} - y = 1

2 x^{3} - x + 1 = 0

4 x^{4} + 8 x^{3} - 17 x^{2} - 21 x - 18 = 0

6 x^{4} - 45 x^{2} + 81 = 0

What are the solutions to the equation x^4+5x^2-14=0 ?
The solutions to the equation x^4+5x^2-14=0 are x=sqrt(2),x=-sqrt(2),x=sqrt(7)i,x=-sqrt(7)i
Find the zeros of x^4+5x^2-14=0
The zeros of x^4+5x^2-14=0 are x=sqrt(2),x=-sqrt(2),x=sqrt(7)i,x=-sqrt(7)i