What are the solutions to the equation 6m^4-15m^2=9 ?

The solutions to the equation 6m^4-15m^2=9 are m=sqrt(3),m=-sqrt(3),m= 1/(sqrt(2))i,m=-1/(sqrt(2))i

Find the zeros of 6m^4-15m^2=9

The zeros of 6m^4-15m^2=9 are m=sqrt(3),m=-sqrt(3),m= 1/(sqrt(2))i,m=-1/(sqrt(2))i

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6 m^{4} - 15 m^{2} = 9

m = 3, m = - 3, m = \frac{1}{2} i, m = - \frac{1}{2} i

Solution steps

6 m^{4} - 15 m^{2} = 9

Move

9

to the left side

6 m^{4} - 15 m^{2} - 9 = 0

Rewrite the equation with

u = m^{2}

and

u^{2} = m^{4}

6 u^{2} - 15 u - 9 = 0

Solve

6 u^{2} - 15 u - 9 = 0 : u = 3, u = - \frac{1}{2}

u = 3, u = - \frac{1}{2}

Substitute back

u = m^{2},

solve for

m

Solve

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

Solve

m^{2} = - \frac{1}{2} : m = \frac{1}{2} i, m = - \frac{1}{2} i

The solutions are

m = 3, m = - 3, m = \frac{1}{2} i, m = - \frac{1}{2} i

(x^{2} + 1) (x - 1) = 0

x^{4} + 8 x^{3} + 3 x - 12 = 0

x^{5} - 2 = 30

(2 x^{2} + 1)^{2} - 4 x^{2} = 0

3 x^{4} + 12 x^{2} = 6 x^{3}

What are the solutions to the equation 6m^4-15m^2=9 ?
The solutions to the equation 6m^4-15m^2=9 are m=sqrt(3),m=-sqrt(3),m= 1/(sqrt(2))i,m=-1/(sqrt(2))i
Find the zeros of 6m^4-15m^2=9
The zeros of 6m^4-15m^2=9 are m=sqrt(3),m=-sqrt(3),m= 1/(sqrt(2))i,m=-1/(sqrt(2))i