Question

What are the real or imaginary solutions of the polynomials `x^4-52x^2+576=0`?

Answer 1

`+-6 and +-4` See the illustrative graph.

Explanation:

`f(x)=(x^2-26)^2-100`. So,

(x^2-26)^2=100#, giving

`x^2=26+-10`

`=36 and 16`

`x=+-6 and +-4`

graph{x^4-52x^2+576 [-7, 7, -3.5, 3.5]}