closed by
399 views
0 votes
0 votes
closed as a duplicate of: ISI2017-MMA-19

If $\alpha, \beta$ and $\gamma$ are the roots of $x^3-px+q=0$, then the value of the determinant $\begin{vmatrix} \alpha & \beta & \gamma \\ \beta & \gamma & \alpha \\ \gamma & \alpha & \beta \end{vmatrix}$ is

  1. $p$
  2. $p^2$
  3. $0$
  4. $p^2+6q$
closed by

Related questions

3 votes
3 votes
2 answers
1
jjayantamahata asked Mar 28, 2018
850 views
If $\alpha, \beta$ and $\gamma$ are the roots of $x^3 - px +q = 0$, then the value of the determinant$$\begin{vmatrix}\alpha & \beta & \gamma\\\beta & \gamma & \alpha\\\g...
0 votes
0 votes
0 answers
2
go_editor asked Sep 15, 2018
609 views
If $A$ is a $2 \times 2$ matrix such that $trace \: A = det \: A =3$, then what is the trace of $A^{-1}$?$1$$1/3$$1/6$$1/2$
0 votes
0 votes
0 answers
3
go_editor asked Sep 15, 2018
375 views
The diagonal elements of a square matrix $M$ are odd integers while the off-diagonals are even integers. Then$M$ must be singular$M$ must be nonsingularthere is not enoug...
0 votes
0 votes
0 answers
4
go_editor asked Sep 15, 2018
487 views
The number of ordered pairs $(X, Y)$, where $X$ and $Y$ are $n \times n$ real, matrices such that $XY-YX=I$ is$0$$1$$n$infinite