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If $ω \neq 1$ is a cube root of unity and
$Δ = |\begin{array}{ccc} x + ω^{2} & ω & 1 \\ ω & ω^{2} & 1 + x \\ 1 & x + ω & ω^{2} \end{array}| = 0$ , then value of $x$ is

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Correct option is A

Applying C1→C1+C2+C3 , we get Δ=x+ω2+ω+1ω1ω+ω2+1+xω21+x1+x+ω+ω2x+ωω2=xω1xω21+xxx+ωω2 using 1 +ω+ω2=0∆is clearly equal to 0 for x = 0.

Similar Questions

If $f (x) = |\begin{array}{ccc} x - 3 & 2 x^{2} - 18 & 3 x^{3} - 81 \\ x - 5 & 2 x^{2} - 50 & 4 x^{3} - 500 \\ 1 & 2 & 3 \end{array}|$ ,then $f (1) \cdot f (3) + f (3) \cdot f (5) \cdot f (5) \cdot f (1)$ is equal to

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