JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Easy

1 of 1

Application +4 | -1

\alpha, \beta

are the roots of

x^2+p x+q=0

, and

\omega

is a cube root of unity, then value of

\left(\omega \alpha+\omega^2 \beta\right)\left(\omega^2 \alpha+\omega \beta\right)

View answer and explanation

Correct option: D

p^2-3 q

Option D (

p^2-3 q

) is correct because, given

\alpha, \beta

are roots of

x^2+p x+q=0

, and

\omega

is a cube root of unity, the expression

(\omega \alpha+\omega^2 \beta)(\omega^2 \alpha+\omega \beta)

simplifies to

p^2 - 3q

using Vieta's formulas.

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