If x is a complex root of the equation | array ccc 1 & x & x x & 1 & x x & x & 1 array |+| array ccc 1-x & 1 & 1 1 & 1-x & 1 1 & 1 & 1-x array |=0 , then x^ 2007 +x^ -2007 =

Correct answer: C. -2 Expanding the two determinants, we get (1-3 x^2+2 x^3)+(3 x^2-x^3)=0 x^3+1=0 x=-ω,-ω^2,-1x^ 2007 +x^ -2007 =-1-1=-2

BITSAT 2024Paper 2

Exam: BITSAT
Year: 2024
Paper: Paper 2
Subject: Mathematics
Chapter: Determinants

BITSAT 2024 · Paper 2 · Mathematics · Determinants

If x is a complex root of the equation | array ccc 1 & x & x x & 1...

x

is a complex root of the equation

\left|

\begin{array}{ccc}1 & x & x \\ x & 1 & x \\ x & x & 1\end{array}

\right|+\left|

\begin{array}{ccc}1-x & 1 & 1 \\ 1 & 1-x & 1 \\ 1 & 1 & 1-x\end{array}

\right|=0

, then

x^{2007}+x^{-2007}=

Options

A $1$
B $-1$
C $-2$
D $2$

Correct answer

C. $-2$

Step-by-step solution

Expanding the two determinants, we get \left(1-3 x^2+2 x^3\right)+\left(3 x^2-x^3\right)=0\Rightarrow x^3+1=0\Rightarrow x=-\omega,-\omega^2,-1x^{2007}+x^{-2007}=-1-1=-2

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