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KonstantinChe [14]
3 years ago
7

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

Mathematics
1 answer:
saveliy_v [14]3 years ago
8 0

Answer:

<u>It</u><u> </u><u>has</u><u> </u><u>two</u><u> </u><u>roots</u>

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

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