Question

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

I don't think there is a solution, i just want to know if I'm right before i proceed

Answer 1

x^4 -­52x^2 + 576 = 0
factor: (x²-36)(x²-16)=0
x²=36 or x²=16
x=6, -6 or x=4, -4
all the solutions are real in this case.

Answer 2

Answer with explanation:

The fourth degree Polynomial is:

`\rightarrow x^4-52x^2+576=0\\\\ \text{Splitting the middle term}\\\\\rightarrow x^4-36x^2-16x^2+576=0\\\\\rightarrow x^2*(x^2-36)-16*(x^2-36)=0\\\\\rightarrow (x^2-16)(x^2-36)=0\\\\\rightarrow (x-4)(x+4)(x-6)(x+6)=0\\\\x=4,-4,6,-6`

There are four real Zeroes of the forth degree Polynomial.