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

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

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

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

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

x = 0, x = \frac{1}{2}, x = - \frac{1}{2}

Solution steps

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

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

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

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

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

Solve

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

u = 0, u = \frac{1}{4}

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = 0 : x = 0

Solve

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

The solutions are

x = 0, x = \frac{1}{2}, x = - \frac{1}{2}

X^{3} = 30 3^{3} + 40 4^{3} + 50 5^{3}

(u^{2} - 6 u + 8) (2 u + 14) = 0

X^{4} - X^{2} + 1 = 0

4 x^{3} = 16 x

1 - 9 x - 6 x - x^{3} = 0

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