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Question: If \(\alpha,\beta\) are non real numbers satisfying \(x^{3} - 1\)=0 then the value of \(\left| \begi...

If α,β\alpha,\beta are non real numbers satisfying x3−1x^{3} - 1=0 then the value of ∣λ+1αβαλ+β1β1λ+α∣\left| \begin{matrix} \lambda + 1 & \alpha & \beta \\ \alpha & \lambda + \beta & 1 \\ \beta & 1 & \lambda + \alpha \end{matrix} \right| is equal to

A

0

B

λ3\lambda^{3}

C

λ3+1\lambda^{3} + 1

D

λ3−1\lambda^{3} - 1

Answer

λ3\lambda^{3}

Explanation

Solution

x3−1=0∴x=1,ω,ω2x^{3} - 1 = 0\therefore x = 1,\omega,\omega^{2};

Here α = ω\omega β=ω2\omega^{2}