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Mathematics 12 Online
LootAtTheTime:

How many complex roots does the equation below have? x ^6 + x ^3 + 1 = 0 The number of complex roots is

LootAtTheTime:

@Zowie @Layla @Vocaloid I need assistance!

Layla:

6 complex roots

LootAtTheTime:

omg you type fast o:

Layla:

sorry about the weird wacky numbers

Layla:

lol

LootAtTheTime:

could you explain :L please

Layla:

Okay so..... hold on

Layla:

|dw:1505925869877:dw|

LootAtTheTime:

ooooooooo ty

Layla:

then let x^3=u then let x^6= u^2

Layla:

The discrimenant is...|dw:1505925993772:dw|

Layla:

which is negative so, u has two complex roots

Layla:

So there are two complex values x3. There are 3 complex cube roots of each of those two complex roots for u. Therefore, there are 6 complex roots.

Layla:

so, that is your answer

LootAtTheTime:

tysm for the explanation

LootAtTheTime:

I get it now

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