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NDA 1 2024 Maths, question 4

Topic: Algebra

Q4

If x,yx,y and zz are the cube roots of unity, then what is the value of xy+yz+zxxy+yz+zx ?

  1. (a) 00Correct answer
  2. (b) 11
  3. (c) 22
  4. (d) 33

Solution.

Answer: (a) 00

  1. The three cube roots are the roots of t³−1=0.
  2. By Vieta's formulas, the sum of their pairwise products is the coefficient of t, namely zero.
  3. Equivalently, with roots 1,ω,ω², the sum is ω+ω²+ω³=0.