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

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

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

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

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

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

Solution steps

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

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

4 u^{2} - 3 u - 1 = 0

Solve

4 u^{2} - 3 u - 1 = 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

x, x^{4} - 7 x^{2} + 6 = 0

5^{3} = (x + 2)^{3}

j^{3} = 0.125

(72) 4 = n^{8}

x, x^{3} - 6 y = 8

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