What are the solutions to the equation 5t^4+15t^2+50=0 ?

The solutions to the equation 5t^4+15t^2+50=0 are

Find the zeros of 5t^4+15t^2+50=0

The zeros of 5t^4+15t^2+50=0 are

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5 t^{4} + 15 t^{2} + 50 = 0

t = \frac{- 3 + 2 10}{2} + \frac{31}{2 - 3 + 2 10} i, t = - \frac{- 3 + 2 10}{2} - \frac{31}{2 - 3 + 2 10} i, t = \frac{- 3 + 2 10}{2} - \frac{31}{2 - 3 + 2 10} i, t = - \frac{- 3 + 2 10}{2} + \frac{31}{2 - 3 + 2 10} i

Solution steps

5 t^{4} + 15 t^{2} + 50 = 0

Rewrite the equation with

u = t^{2}

and

u^{2} = t^{4}

5 u^{2} + 15 u + 50 = 0

Solve

5 u^{2} + 15 u + 50 = 0 : u = - \frac{3}{2} + i \frac{31}{2}, u = - \frac{3}{2} - i \frac{31}{2}

u = - \frac{3}{2} + i \frac{31}{2}, u = - \frac{3}{2} - i \frac{31}{2}

Substitute back

u = t^{2},

solve for

t

Solve

t^{2} = - \frac{3}{2} + i \frac{31}{2} : t = \frac{- 3 + 2 10}{2} + \frac{31}{2 - 3 + 2 10} i, t = - \frac{- 3 + 2 10}{2} - \frac{31}{2 - 3 + 2 10} i

Solve

t^{2} = - \frac{3}{2} - i \frac{31}{2} : t = \frac{- 3 + 2 10}{2} - \frac{31}{2 - 3 + 2 10} i, t = - \frac{- 3 + 2 10}{2} + \frac{31}{2 - 3 + 2 10} i

The solutions are

t = \frac{- 3 + 2 10}{2} + \frac{31}{2 - 3 + 2 10} i, t = - \frac{- 3 + 2 10}{2} - \frac{31}{2 - 3 + 2 10} i, t = \frac{- 3 + 2 10}{2} - \frac{31}{2 - 3 + 2 10} i, t = - \frac{- 3 + 2 10}{2} + \frac{31}{2 - 3 + 2 10} i

x^{8} = 9

- 4 x^{3} + 24 x = 0

x^{4} + x = 3

x^{3} = 13 x^{2} - 42 x

s^{3} + 3 s^{2} + 3 s - 7 = 0

What are the solutions to the equation 5t^4+15t^2+50=0 ?
The solutions to the equation 5t^4+15t^2+50=0 are
Find the zeros of 5t^4+15t^2+50=0
The zeros of 5t^4+15t^2+50=0 are