1. Tardigrade
  2. Question
  3. Mathematics
  4. Let A=[β γ-α2 γ α-β2 α β-γ2 γ α-β2 α β-γ2 β γ-α2 α β-γ2 β γ-α2 γ α-β2] where α, β, γ are roots of the equation x3-2 x2+2 x-3=0 Now, consider f(x)=|A-x I|, where I is identity matrix of order 3 . The sum of the roots of the equation f(x)=0, is-

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Q. Let $A=\begin{bmatrix}\beta \gamma-\alpha^2 & \gamma \alpha-\beta^2 & \alpha \beta-\gamma^2 \\ \gamma \alpha-\beta^2 & \alpha \beta-\gamma^2 & \beta \gamma-\alpha^2 \\ \alpha \beta-\gamma^2 & \beta \gamma-\alpha^2 & \gamma \alpha-\beta^2\end{bmatrix}$ where $\alpha, \beta, \gamma$ are roots of the equation $x^3-2 x^2+2 x-3=0$ Now, consider $f(x)=|A-x I|$, where $I$ is identity matrix of order 3 .
The sum of the roots of the equation $f(x)=0$, is-

Matrices

Solution:

Correct answer is (d) 2