What are the solutions to the equation 4x^4+5x^2-9=0 ?

The solutions to the equation 4x^4+5x^2-9=0 are x=1,x=-1,x= 3/2 i,x=-3/2 i

Find the zeros of 4x^4+5x^2-9=0

The zeros of 4x^4+5x^2-9=0 are x=1,x=-1,x= 3/2 i,x=-3/2 i

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4 x^{4} + 5 x^{2} - 9 = 0

x = 1, x = - 1, x = \frac{3}{2} i, x = - \frac{3}{2} i

Solution steps

4 x^{4} + 5 x^{2} - 9 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

4 u^{2} + 5 u - 9 = 0

Solve

4 u^{2} + 5 u - 9 = 0 : u = 1, u = - \frac{9}{4}

u = 1, u = - \frac{9}{4}

Substitute back

u = x^{2},

solve for

x

Solve

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

Solve

x^{2} = - \frac{9}{4} : x = \frac{3}{2} i, x = - \frac{3}{2} i

The solutions are

x = 1, x = - 1, x = \frac{3}{2} i, x = - \frac{3}{2} i

(x^{2} + 4 x)^{2} - 17 (x^{2} + 4 x) = 60

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

x, x^{3} - 6 x^{2} + 6 x + 5 = 0

(z^{3} + i - 1) (1 - 2 z + 2 z^{2}) = 0

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

What are the solutions to the equation 4x^4+5x^2-9=0 ?
The solutions to the equation 4x^4+5x^2-9=0 are x=1,x=-1,x= 3/2 i,x=-3/2 i
Find the zeros of 4x^4+5x^2-9=0
The zeros of 4x^4+5x^2-9=0 are x=1,x=-1,x= 3/2 i,x=-3/2 i