What are the solutions to the equation 12x^4-9x^2-3=0 ?

The solutions to the equation 12x^4-9x^2-3=0 are x=1,x=-1,x= 1/2 i,x=-1/2 i

Find the zeros of 12x^4-9x^2-3=0

The zeros of 12x^4-9x^2-3=0 are x=1,x=-1,x= 1/2 i,x=-1/2 i

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12 x^{4} - 9 x^{2} - 3 = 0

x = 1, x = - 1, x = \frac{1}{2} i, x = - \frac{1}{2} i

Solution steps

12 x^{4} - 9 x^{2} - 3 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

12 u^{2} - 9 u - 3 = 0

Solve

12 u^{2} - 9 u - 3 = 0 : u = 1, u = - \frac{1}{4}

u = 1, u = - \frac{1}{4}

Substitute back

u = x^{2},

solve for

x

Solve

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

Solve

x^{2} = - \frac{1}{4} : x = \frac{1}{2} i, x = - \frac{1}{2} i

The solutions are

x = 1, x = - 1, x = \frac{1}{2} i, x = - \frac{1}{2} i

5 = c^{3}

x^{3} - 9 x + 10 = 0

x^{5} - 2 x^{4} + 1 = 0

2 x^{3} = - 128

- 2 x^{4} + 9 = 2 x + 3

What are the solutions to the equation 12x^4-9x^2-3=0 ?
The solutions to the equation 12x^4-9x^2-3=0 are x=1,x=-1,x= 1/2 i,x=-1/2 i
Find the zeros of 12x^4-9x^2-3=0
The zeros of 12x^4-9x^2-3=0 are x=1,x=-1,x= 1/2 i,x=-1/2 i