Roots of unity for beginners 2
Algebra
Level
4
How many roots have an integral real part for
2
0
4
1
3
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1 solution
Let p ( x ) = x 3 + x 2 + x + 1 = 0
By Rational Root Theorm , we found that x = − 1 is a root of p ( x ) , so we can factor it out :
( x + 1 ) ( x 2 + 1 ) = 0
so roots are − 1 , i , − i and there real parts are − 1 , 0 , 0 respectively. So answer is 3.