What are the solutions to the equation 10x^4-3x^2+1=0 ?

The solutions to the equation 10x^4-3x^2+1=0 are

Find the zeros of 10x^4-3x^2+1=0

The zeros of 10x^4-3x^2+1=0 are

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10 x^{4} - 3 x^{2} + 1 = 0

x = \frac{3 + 2 10}{2 10} + \frac{31}{2 10 3 + 2 10} i, x = - \frac{3 + 2 10}{2 10} - \frac{31}{2 10 3 + 2 10} i, x = \frac{3 + 2 10}{2 10} - \frac{31}{2 10 3 + 2 10} i, x = - \frac{3 + 2 10}{2 10} + \frac{31}{2 10 3 + 2 10} i

Solution steps

10 x^{4} - 3 x^{2} + 1 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

10 u^{2} - 3 u + 1 = 0

Solve

10 u^{2} - 3 u + 1 = 0 : u = \frac{3}{20} + i \frac{31}{20}, u = \frac{3}{20} - i \frac{31}{20}

u = \frac{3}{20} + i \frac{31}{20}, u = \frac{3}{20} - i \frac{31}{20}

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = \frac{3}{20} + i \frac{31}{20} : x = \frac{3 + 2 10}{2 10} + \frac{31}{2 10 3 + 2 10} i, x = - \frac{3 + 2 10}{2 10} - \frac{31}{2 10 3 + 2 10} i

Solve

x^{2} = \frac{3}{20} - i \frac{31}{20} : x = \frac{3 + 2 10}{2 10} - \frac{31}{2 10 3 + 2 10} i, x = - \frac{3 + 2 10}{2 10} + \frac{31}{2 10 3 + 2 10} i

The solutions are

x = \frac{3 + 2 10}{2 10} + \frac{31}{2 10 3 + 2 10} i, x = - \frac{3 + 2 10}{2 10} - \frac{31}{2 10 3 + 2 10} i, x = \frac{3 + 2 10}{2 10} - \frac{31}{2 10 3 + 2 10} i, x = - \frac{3 + 2 10}{2 10} + \frac{31}{2 10 3 + 2 10} i

x^{3} + 7 x^{2} - 4 x - 28 = 0

x^{4} - 2 x^{3} + x^{2} - 8 x - 12 = 0

3 x^{3} + 15 x^{2} = 18 x

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

12 x^{3} - 20 x^{2} + 11 x - 2 = 0

What are the solutions to the equation 10x^4-3x^2+1=0 ?
The solutions to the equation 10x^4-3x^2+1=0 are
Find the zeros of 10x^4-3x^2+1=0
The zeros of 10x^4-3x^2+1=0 are