Question

What are the real and complex solutions of the polynomial equation?
x^4-41x^2=-400

Answer 1

x^4 - 41x^2 + 400 = 0 : standard form equation

The solutions of this equation are:
X1 = 4
X2 = -4
X3 = 5
X4 = -5

there are many ways to solve this, but I'd just graph it if possible and the intercepts are clearly those 4 solutions

Answer 2

Can I have the steps on how you did that?

Answer 3

there are many methods but i simply typed the equation

https://www.desmos.com/calculator

Answer 4

you might be able to do algebraically etc

Answer 5

I figured it out but thank you!

Answer 6

this is an equation that can be written as a quadratic and then factored.

\[(x^2)^2 - 41x^2 + 400 = 0\]

the factors of 400 that add to -41 and -25 and -16

so in factored from its

\[(x^2 -16)(x^2 - 25) = 0\]

the quadratic factors are the difference of 2 squares, so can be factored and solutions found

hope it helps

Answer 7

yep, that's another method^

Answer 8

Technically, all the roots are complex :P

Answer 9

@uhhh how can

\[x^2 - 16 = 0 ~~~and~~~~x^2 - 25 = 0\]

have complex roots

Answer 10

4 is a complex number and a real number
-4 is a complex number and a real number
5 is a complex number and a real number
-5 is a complex number and a real number

Answer 11

All real numbers are complex. All imaginary numbers are complex. Sums of real and imaginary numbers are also complex.