Posted by lee on Sunday, November 18, 2012 at 10:19am.
First byou must find real solution.
x ^ 3 - 8 = 0 Add 8 to both sides
x ^ 3 - 8 + 8 = 0 + 8
x ^ 3 = 8
x = third root of 8 = 2
In this case one rational zero is x = 2
Now you divide polynomial x ^ 3 - 8 with ( x - 2 )
( x ^ 3 - 8 ) / ( x - 2 ) = x ^ 2 + 2 x + 4
OR
( x ^ 3 - 8 ) = ( x ^ 2 + 2 x + 4 ) * ( x - 2 ) = 0
Youe equation have roots when :
x ^ 2 + 2 x + 4 = 0
AND
x - 2 = 0
Solutions of equation x ^ 2 + 2 x + 4 = 0
are
1 + i sgrt 3 and 1 - i sgrt 3
Soluton of equation x - 2 = 0
are
x = 2
Your equation have 3 solutions.
One real solution x = 2
and two imaginary solutions :
1 + i sgrt 3 and 1 - i sgrt 3
thank you
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