What are the solutions to the equation roots x^6+5x^3+6 ?

The solutions to the equation roots x^6+5x^3+6 are

Find the zeros of roots x^6+5x^3+6

The zeros of roots x^6+5x^3+6 are

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roots

x^{6} + 5 x^{3} + 6

Solution steps

x^{6} + 5 x^{3} + 6

The roots are the intercepts with the x-axis

(y = 0)

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

Rewrite the equation with

u = x^{3}

and

u^{2} = x^{6}

u^{2} + 5 u + 6 = 0

Solve

u^{2} + 5 u + 6 = 0 : u = - 2, u = - 3

u = - 2, u = - 3

Substitute back

u = x^{3},

solve for

x

Solve

The solutions are

y, x = y^{3}

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

(x - 3)^{4} - 8 (x - 3)^{2} - 9 = 0

y, y^{2} = x^{3}

y, x^{3} + y^{3} = 1

What are the solutions to the equation roots x^6+5x^3+6 ?
The solutions to the equation roots x^6+5x^3+6 are
Find the zeros of roots x^6+5x^3+6
The zeros of roots x^6+5x^3+6 are