What are the solutions to the equation 15x^4-12x^2-3=0 ?

The solutions to the equation 15x^4-12x^2-3=0 are x=1,x=-1,x= 1/(sqrt(5))i,x=-1/(sqrt(5))i

Find the zeros of 15x^4-12x^2-3=0

The zeros of 15x^4-12x^2-3=0 are x=1,x=-1,x= 1/(sqrt(5))i,x=-1/(sqrt(5))i

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15 x^{4} - 12 x^{2} - 3 = 0

x = 1, x = - 1, x = \frac{1}{5} i, x = - \frac{1}{5} i

Solution steps

15 x^{4} - 12 x^{2} - 3 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

15 u^{2} - 12 u - 3 = 0

Solve

15 u^{2} - 12 u - 3 = 0 : u = 1, u = - \frac{1}{5}

u = 1, u = - \frac{1}{5}

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = 1 : x = 1, x = - 1

Solve

x^{2} = - \frac{1}{5} : x = \frac{1}{5} i, x = - \frac{1}{5} i

The solutions are

x = 1, x = - 1, x = \frac{1}{5} i, x = - \frac{1}{5} i

x^{4} + 25 = 26 x^{2}

2 x^{3} - 3 x^{2} - 11 x + 6

x^{4} = 5 x + 6

x^{3} + 8 x^{2} - 36 x = 288

x^{3} - 9 x^{2} + 27 x = 20

What are the solutions to the equation 15x^4-12x^2-3=0 ?
The solutions to the equation 15x^4-12x^2-3=0 are x=1,x=-1,x= 1/(sqrt(5))i,x=-1/(sqrt(5))i
Find the zeros of 15x^4-12x^2-3=0
The zeros of 15x^4-12x^2-3=0 are x=1,x=-1,x= 1/(sqrt(5))i,x=-1/(sqrt(5))i