Question

How many solutions equation x^4 + 2x^2 - 15 = 0 has?

Answer 1

x ^ 4 + 2 x ^ 2 - 15 = 0

Substitute :

u = x ^ 2

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Remark :

If u = x ^ 2 then x ^ 4 = u ^ 2
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You must solve equation :

u ^ 2 + 2 u - 15 = 0

The exact solutions are :

u = 3

and

u = - 5


So solutions are :

x ^ 2 = 3

x = sqrt ( 3 )

x = - sqrt ( 3 )


x ^ 2 = - 5

x = sqrt ( - 5 ) = i sqrt ( 5 )

x = - sqrt ( - 5 ) = - i sqrt ( 5 )


Equation :

x ^ 4 + 2 x ^ 2 - 15 = 0

has 4 solutions ( 2 real and 2 imaginary )


P.S.

If you don't know how to solve equation :

u ^ 2 + 2 u - 15 = 0

In google type:

quadratic equation online

When you see list of results click on:
Free Online Quadratic Equation Solver:Solve by Quadratic Formula

When page be open in rectangle type:

u ^ 2 + 2 u - 15 = 0

and click option: solve it

You will see solution step-by step