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

Jan 14, 2017

$\pm 6 \mathmr{and} \pm 4$ See the illustrative graph.

#### Explanation:

$f \left(x\right) = {\left({x}^{2} - 26\right)}^{2} - 100$. So,

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

${x}^{2} = 26 \pm 10$

$= 36 \mathmr{and} 16$

$x = \pm 6 \mathmr{and} \pm 4$

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