If 1, x 1 , x 2 , x 3 are the roots of x 4 - 1 = 0 and ω is an imaginary cube root of…
Mathematics · JEE Advanced · NTA Exams — Complex Numbers and Quadratic Equations
If 1, x1, x2, x3 are the roots of x4 - 1 = 0 and ω is an imaginary cube root of unity, then the value of
\(\frac{\left(\omega^{2}-x_{1}\right)\left(\omega^{2}-x_{2}\right)\left(\omega^{2}-x_{3}\right)}{\left(\omega-x_{1}\right)\left(\omega-x_{2}\right)\left(\omega-x_{3}\right)}\) is
\(\frac{\left(\omega^{2}-x_{1}\right)\left(\omega^{2}-x_{2}\right)\left(\omega^{2}-x_{3}\right)}{\left(\omega-x_{1}\right)\left(\omega-x_{2}\right)\left(\omega-x_{3}\right)}\) is
- \(1\)
- \(-1\)
- \(\omega\)
- \(\omega^2\)
Answer
(A) 1
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