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

The solutions to the equation 2x^2-x^4=0 are x=0,x=sqrt(2),x=-sqrt(2)

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

The zeros of 2x^2-x^4=0 are x=0,x=sqrt(2),x=-sqrt(2)

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

x = 0, x = 2, x = - 2

Decimal Notation

x = 0, x = 1.41421 \dots, x = - 1.41421 \dots

Solution steps

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

Write in the standard form

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

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

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

- u^{2} + 2 u = 0

Solve

- u^{2} + 2 u = 0 : u = 0, u = 2

u = 0, u = 2

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = 0 : x = 0

Solve

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

The solutions are

x = 0, x = 2, x = - 2

x^{5} - 5 x^{3} = 0

12 x^{5} - 108 x^{3} = 0

e = 1.6 \times 10 e^{12}

x, 0 = x^{4} - 12 x^{3} - 42 x^{2} + 11

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

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