What are the solutions to the equation 2k^4-3k^2+5=25 ?

The solutions to the equation 2k^4-3k^2+5=25 are k=2,k=-2,k=sqrt(5/2)i,k=-sqrt(5/2)i

Find the zeros of 2k^4-3k^2+5=25

The zeros of 2k^4-3k^2+5=25 are k=2,k=-2,k=sqrt(5/2)i,k=-sqrt(5/2)i

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2 k^{4} - 3 k^{2} + 5 = 25

k = 2, k = - 2, k = \frac{5}{2} i, k = - \frac{5}{2} i

Solution steps

2 k^{4} - 3 k^{2} + 5 = 25

Move

25

to the left side

2 k^{4} - 3 k^{2} - 20 = 0

Rewrite the equation with

u = k^{2}

and

u^{2} = k^{4}

2 u^{2} - 3 u - 20 = 0

Solve

2 u^{2} - 3 u - 20 = 0 : u = 4, u = - \frac{5}{2}

u = 4, u = - \frac{5}{2}

Substitute back

u = k^{2},

solve for

k

Solve

k^{2} = 4 : k = 2, k = - 2

Solve

k^{2} = - \frac{5}{2} : k = \frac{5}{2} i, k = - \frac{5}{2} i

The solutions are

k = 2, k = - 2, k = \frac{5}{2} i, k = - \frac{5}{2} i

x^{4} + 3 x^{2} - 18 = 0

x (2 x^{2} + x - 3) = 10

5 x^{3} + 20 x^{2} + 20 x = 0

x^{5} - 5 x = - 1

x^{5} - 5 x = - 4

What are the solutions to the equation 2k^4-3k^2+5=25 ?
The solutions to the equation 2k^4-3k^2+5=25 are k=2,k=-2,k=sqrt(5/2)i,k=-sqrt(5/2)i
Find the zeros of 2k^4-3k^2+5=25
The zeros of 2k^4-3k^2+5=25 are k=2,k=-2,k=sqrt(5/2)i,k=-sqrt(5/2)i