What are the solutions to the equation 24x^4-8x^2+30=0 ?

The solutions to the equation 24x^4-8x^2+30=0 are

Find the zeros of 24x^4-8x^2+30=0

The zeros of 24x^4-8x^2+30=0 are

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24 x^{4} - 8 x^{2} + 30 = 0

x = \frac{1 + 3 5}{2 3} + \frac{11}{3 1 + 3 5} i, x = - \frac{1 + 3 5}{2 3} - \frac{11}{3 1 + 3 5} i, x = \frac{1 + 3 5}{2 3} - \frac{11}{3 1 + 3 5} i, x = - \frac{1 + 3 5}{2 3} + \frac{11}{3 1 + 3 5} i

Solution steps

24 x^{4} - 8 x^{2} + 30 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

24 u^{2} - 8 u + 30 = 0

Solve

24 u^{2} - 8 u + 30 = 0 : u = \frac{1}{6} + i \frac{11}{3}, u = \frac{1}{6} - i \frac{11}{3}

u = \frac{1}{6} + i \frac{11}{3}, u = \frac{1}{6} - i \frac{11}{3}

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = \frac{1}{6} + i \frac{11}{3} : x = \frac{1 + 3 5}{2 3} + \frac{11}{3 1 + 3 5} i, x = - \frac{1 + 3 5}{2 3} - \frac{11}{3 1 + 3 5} i

Solve

x^{2} = \frac{1}{6} - i \frac{11}{3} : x = \frac{1 + 3 5}{2 3} - \frac{11}{3 1 + 3 5} i, x = - \frac{1 + 3 5}{2 3} + \frac{11}{3 1 + 3 5} i

The solutions are

x = \frac{1 + 3 5}{2 3} + \frac{11}{3 1 + 3 5} i, x = - \frac{1 + 3 5}{2 3} - \frac{11}{3 1 + 3 5} i, x = \frac{1 + 3 5}{2 3} - \frac{11}{3 1 + 3 5} i, x = - \frac{1 + 3 5}{2 3} + \frac{11}{3 1 + 3 5} i

x^{3} + 3 x^{2} - 14 x - 42 = 0

4 x^{4} = 13 x^{2} - 9

a^{9} = 17 + (9 - 1) - 8

- x^{3} + 3 x^{2} + 24 x - 80 = 0

- x^{3} - 67 x^{2} - 185 x - 10 = 0

What are the solutions to the equation 24x^4-8x^2+30=0 ?
The solutions to the equation 24x^4-8x^2+30=0 are
Find the zeros of 24x^4-8x^2+30=0
The zeros of 24x^4-8x^2+30=0 are