QJEEM24Ma275d: JEE Main 2024 Mathematics - Class 11 JEEM24Ma275d Solution: If satisfies the equation and , then is equal to ____________.

Question

Verified Solution • 2025–26 Session moderate

If

\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 ____________.

Accepted Answer

$x^{2} + x + 1 = 0 \Rightarrow x = ω, ω^{2} = α$

Let $α = ω$

Now $(1 + α)^{7} = - ω^{14} = - ω^{2} = 1 + ω$

$\begin{aligned} A = 1, B = 1, C = 0 \\ ∴ 5 (3 A - 2 B - C) = 5 (3 - 2 - 0) = 5 \end{aligned}$

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