Question

F(x) = (x2 + 6)2 has how many
roots.

Answer 1

It has two roots

that is †2.4i and -2.4i

Explanation:

`f(x) = ( {x}^(2) + 6) {}^(2)`

for a root, f(x) is zero

`{( {x}^(2) + 6)}^(2) = 0 \\ ( {x}^(2) + 6) = 0`

subtract 6 from both sides:

`( {x}^(2) + 6) - 6 = 0 - 6 \\ {x}^(2) = - 6`

remember: from complex numbers, i² is -1

`{x}^(2) = 6 {i}^(2)`

take square root on both sides:

`\sqrt{ {x}^(2) } = \sqrt{ {6i}^(2) } \\ x = i √(6) \\ x = + 2.4i \: \: and \: \: - 2.4i`