Answer:
It has two roots
that is †2.4i and -2.4i
Step-by-step explanation:
[tex]f(x) = ( {x}^{2} + 6) {}^{2} [/tex]
for a root, f(x) is zero
[tex] {( {x}^{2} + 6)}^{2} = 0 \\ ( {x}^{2} + 6) = 0[/tex]
subtract 6 from both sides:
[tex]( {x}^{2} + 6) - 6 = 0 - 6 \\ {x}^{2} = - 6[/tex]
remember: from complex numbers, i² is -1
[tex] {x}^{2} = 6 {i}^{2} [/tex]
take square root on both sides:
[tex] \sqrt{ {x}^{2} } = \sqrt{ {6i}^{2} } \\ x = i \sqrt{6} \\ x = + 2.4i \: \: and \: \: - 2.4i[/tex]
