Question

What are the real or imaginary solutions of the polynomial equation x*4-25=0​

Answer 1

Hello from MrBillDoesMath!

Answer:

Solutions: x = +\- 5i or x = +\- sqrt(5)

Discussion:

Factor x^4 - 25:

x^4 - 25 = (x^2+5) (x^2-5) => factor x^2 - 5

x^4 - 25 = (x^2+5)(x + sqrt(5)) (x - sqrt(5)) => factor x^2 + 5

x^4 = 25 = (x +5i)(x-5i) (x + sqrt(5)) (x - sqrt(5))

Hence the solutions are

x = +\- 5i and x = +\- sqrt(5)

Thank you,

MrB