If α satisfies the equation x²+x+1=0 and (1+α)⁷=A+B α+C α², A, B, C 0, then 5(3 A-2 B-C) is equal to _ _ _ _ _ _.

Complex Numbers and Quadratic Equations: JEE Main 2024 Mathematics question

JEE Main 2024 · 27 Jan, Morning shift · Q30

JEE Main 202427 Jan, Morning shiftMathematicsMediumComplex Numbers and Quadratic Equations264× since 2002

\alpha

satisfies the equation

x^2+x+1=0

and

(1+\alpha)^7=A+B \alpha+C \alpha^2, A, B, C \geqslant 0

, then

5(3 A-2 B-C)

is equal to ____________.

Your answerType your answer. Integers and decimals are accepted.