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

The solutions to the equation 2w^4-5w^2+2=0 are w=sqrt(2),w=-sqrt(2),w= 1/(sqrt(2)),w=-1/(sqrt(2))

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

The zeros of 2w^4-5w^2+2=0 are w=sqrt(2),w=-sqrt(2),w= 1/(sqrt(2)),w=-1/(sqrt(2))

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2 w^{4} - 5 w^{2} + 2 = 0

w = 2, w = - 2, w = \frac{1}{2}, w = - \frac{1}{2}

Decimal Notation

w = 1.41421 \dots, w = - 1.41421 \dots, w = 0.70710 \dots, w = - 0.70710 \dots

Solution steps

2 w^{4} - 5 w^{2} + 2 = 0

Rewrite the equation with

u = w^{2}

and

u^{2} = w^{4}

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

Solve

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

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

Substitute back

u = w^{2},

solve for

w

Solve

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

Solve

w^{2} = \frac{1}{2} : w = \frac{1}{2}, w = - \frac{1}{2}

The solutions are

w = 2, w = - 2, w = \frac{1}{2}, w = - \frac{1}{2}

m^{3} - 7 m + 6 = 0

\frac{x ^{4}}{3} = 8

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

m^{6} - 1 = 0

x^{4} + 5 x^{3} + 8 x^{2} - 5 x + 1 = 0

What are the solutions to the equation 2w^4-5w^2+2=0 ?
The solutions to the equation 2w^4-5w^2+2=0 are w=sqrt(2),w=-sqrt(2),w= 1/(sqrt(2)),w=-1/(sqrt(2))
Find the zeros of 2w^4-5w^2+2=0
The zeros of 2w^4-5w^2+2=0 are w=sqrt(2),w=-sqrt(2),w= 1/(sqrt(2)),w=-1/(sqrt(2))