Step-by-step explanation:
Solve for all roots x:
[tex] {x}^{4} - {x}^{2} - 6[/tex]
Substitute
[tex]y = {x}^{2} \\ {y}^{2} - y - 6 = 0[/tex]
The above factors into a product with two terms:
[tex](y - 3)(y + 2) = 0[/tex]
Split into two equations:
[tex]y - 3 = 0 \: \: \: or \: \: \: y + 2 = 0 \\ y = 3 \: \: \: or \: \: \: y = - 2[/tex]
Substitute back
[tex]y = {x}^{2} \\ {x}^{2}=3\: \: \: or \: \: \: {x}^{2}=-2 \\ {x}^{2}=3\\x= \sqrt{3} \: \: \: or \: \: \: x=-\sqrt{3}\\{x}^{2}=-2\\x=i\sqrt{2} \: \: \: or \: \: \: x=-i\sqrt{2}[/tex]
