What are the solutions to the equation roots x^4-7x^2-18 ?

The solutions to the equation roots x^4-7x^2-18 are x=3,x=-3,x=sqrt(2)i,x=-sqrt(2)i

Find the zeros of roots x^4-7x^2-18

The zeros of roots x^4-7x^2-18 are x=3,x=-3,x=sqrt(2)i,x=-sqrt(2)i

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roots

x^{4} - 7 x^{2} - 18

x = 3, x = - 3, x = 2 i, x = - 2 i

Solution steps

x^{4} - 7 x^{2} - 18

The roots are the intercepts with the x-axis

(y = 0)

x^{4} - 7 x^{2} - 18 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

u^{2} - 7 u - 18 = 0

Solve

u^{2} - 7 u - 18 = 0 : u = 9, u = - 2

u = 9, u = - 2

Substitute back

u = x^{2},

solve for

x

Solve

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

Solve

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

The solutions are

x = 3, x = - 3, x = 2 i, x = - 2 i

x^{4} = 2 x^{2}

x^{3} + 512 = 0

x^{3} - 5 x - 8 = 0

4 x + 8 = 2 x^{3}

x^{4} - 2 x^{3} - 10 x^{2} + 18 x + 9 = 0

What are the solutions to the equation roots x^4-7x^2-18 ?
The solutions to the equation roots x^4-7x^2-18 are x=3,x=-3,x=sqrt(2)i,x=-sqrt(2)i
Find the zeros of roots x^4-7x^2-18
The zeros of roots x^4-7x^2-18 are x=3,x=-3,x=sqrt(2)i,x=-sqrt(2)i