What are the solutions to the equation 63-27w^2+2w^4=0 ?

The solutions to the equation 63-27w^2+2w^4=0 are w=sqrt(21/2),w=-sqrt(21/2),w=sqrt(3),w=-sqrt(3)

Find the zeros of 63-27w^2+2w^4=0

The zeros of 63-27w^2+2w^4=0 are w=sqrt(21/2),w=-sqrt(21/2),w=sqrt(3),w=-sqrt(3)

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63 - 27 w^{2} + 2 w^{4} = 0

w = \frac{21}{2}, w = - \frac{21}{2}, w = 3, w = - 3

Decimal Notation

w = 3.24037 \dots, w = - 3.24037 \dots, w = 1.73205 \dots, w = - 1.73205 \dots

Solution steps

63 - 27 w^{2} + 2 w^{4} = 0

Write in the standard form

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

2 w^{4} - 27 w^{2} + 63 = 0

Rewrite the equation with

u = w^{2}

and

u^{2} = w^{4}

2 u^{2} - 27 u + 63 = 0

Solve

2 u^{2} - 27 u + 63 = 0 : u = \frac{21}{2}, u = 3

u = \frac{21}{2}, u = 3

Substitute back

u = w^{2},

solve for

w

Solve

w^{2} = \frac{21}{2} : w = \frac{21}{2}, w = - \frac{21}{2}

Solve

w^{2} = 3 : w = 3, w = - 3

The solutions are

w = \frac{21}{2}, w = - \frac{21}{2}, w = 3, w = - 3

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

8 w^{3} + 2 w - 1 = 0

m^{3} + m^{2} - m - 1 = 0

x^{2} - 6 = 6 - x^{3}

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

What are the solutions to the equation 63-27w^2+2w^4=0 ?
The solutions to the equation 63-27w^2+2w^4=0 are w=sqrt(21/2),w=-sqrt(21/2),w=sqrt(3),w=-sqrt(3)
Find the zeros of 63-27w^2+2w^4=0
The zeros of 63-27w^2+2w^4=0 are w=sqrt(21/2),w=-sqrt(21/2),w=sqrt(3),w=-sqrt(3)