Relations between Roots and Coefficients : Higher Order Equations
If 1,α ,α 2...
Question
If 1,α,α2.....αn−1 are n roots of unity then ,1.α.α2....αn−1 equals
A
(−1)n−1
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B
0
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C
1
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D
-1
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Solution
The correct option is A(−1)n−1 1,α,α2...αn−1 are the nth roots of unity. Thus, they are solutions of the equation: xn−1=0. Thus, product of roots =(−1)n∗(−11) (i.e. (−1)n∗constant term / coefficient ofxn) Thus, the product = (−1)n∗(−11)=(−1)n∗(−11)=(−1)n+1=(−1)2∗(−1)n−1=1∗(−1)n−1=(−1)n−1 Hence, (A) is correct.