What are the solutions to the equation 3x^4-15x^2+29=0 ?

The solutions to the equation 3x^4-15x^2+29=0 are

Find the zeros of 3x^4-15x^2+29=0

The zeros of 3x^4-15x^2+29=0 are

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3 x^{4} - 15 x^{2} + 29 = 0

x = \frac{15 + 2 87}{2 3} + \frac{41}{2 15 + 2 87} i, x = - \frac{15 + 2 87}{2 3} - \frac{41}{2 15 + 2 87} i, x = \frac{15 + 2 87}{2 3} - \frac{41}{2 15 + 2 87} i, x = - \frac{15 + 2 87}{2 3} + \frac{41}{2 15 + 2 87} i

Solution steps

3 x^{4} - 15 x^{2} + 29 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

3 u^{2} - 15 u + 29 = 0

Solve

3 u^{2} - 15 u + 29 = 0 : u = \frac{5}{2} + i \frac{123}{6}, u = \frac{5}{2} - i \frac{123}{6}

u = \frac{5}{2} + i \frac{123}{6}, u = \frac{5}{2} - i \frac{123}{6}

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = \frac{5}{2} + i \frac{123}{6} : x = \frac{15 + 2 87}{2 3} + \frac{41}{2 15 + 2 87} i, x = - \frac{15 + 2 87}{2 3} - \frac{41}{2 15 + 2 87} i

Solve

x^{2} = \frac{5}{2} - i \frac{123}{6} : x = \frac{15 + 2 87}{2 3} - \frac{41}{2 15 + 2 87} i, x = - \frac{15 + 2 87}{2 3} + \frac{41}{2 15 + 2 87} i

The solutions are

x = \frac{15 + 2 87}{2 3} + \frac{41}{2 15 + 2 87} i, x = - \frac{15 + 2 87}{2 3} - \frac{41}{2 15 + 2 87} i, x = \frac{15 + 2 87}{2 3} - \frac{41}{2 15 + 2 87} i, x = - \frac{15 + 2 87}{2 3} + \frac{41}{2 15 + 2 87} i

a^{3} - 3 a^{2} = 240

s^{5} - s^{3} - s^{2} + 1 = 0

a^{5} = 7

x^{4} + x^{3} + x + 1 = 4 x^{2}

x^{4} - 18 x^{2} + 32 = 0

What are the solutions to the equation 3x^4-15x^2+29=0 ?
The solutions to the equation 3x^4-15x^2+29=0 are
Find the zeros of 3x^4-15x^2+29=0
The zeros of 3x^4-15x^2+29=0 are