Question

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

Answer 1

Answer:

It has two roots

that is †2.4i and -2.4i

Step-by-step 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:

$\sqrt{ {x}^{2} } = \sqrt{ {6i}^{2} } \\ x = i \sqrt{6} \\ x = + 2.4i \: \: and \: \: - 2.4i$