What are the solutions to the equation 4x^4+7x^2-2=0 ?

The solutions to the equation 4x^4+7x^2-2=0 are x= 1/2 ,x=-1/2 ,x=sqrt(2)i,x=-sqrt(2)i

Find the zeros of 4x^4+7x^2-2=0

The zeros of 4x^4+7x^2-2=0 are x= 1/2 ,x=-1/2 ,x=sqrt(2)i,x=-sqrt(2)i

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

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

Solution steps

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

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

4 u^{2} + 7 u - 2 = 0

Solve

4 u^{2} + 7 u - 2 = 0 : u = \frac{1}{4}, u = - 2

u = \frac{1}{4}, u = - 2

Substitute back

u = x^{2},

solve for

x

Solve

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

Solve

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

The solutions are

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

- 4 (2 x - 6) = 10 x

10 m^{3} + 4 m^{2} - 90 m - 36

4 m^{2} - 4 mn + n^{2}

- x^{2} - 6 x + 16

\frac{180}{3}

What are the solutions to the equation 4x^4+7x^2-2=0 ?
The solutions to the equation 4x^4+7x^2-2=0 are x= 1/2 ,x=-1/2 ,x=sqrt(2)i,x=-sqrt(2)i
Find the zeros of 4x^4+7x^2-2=0
The zeros of 4x^4+7x^2-2=0 are x= 1/2 ,x=-1/2 ,x=sqrt(2)i,x=-sqrt(2)i