The sum of the real roots of the equation 

\begin{vmatrix} x & -6 &-1 \\ 2 &-3x &x-3 \\ -3& 2x &x+2 \end{vmatrix}=0, is equal to : 

  • Option 1)

    6

  • Option 2)

    0

  • Option 3)

    1

  • Option 4)

    -4

Answers (1)

\begin{vmatrix} x & -6 &-1 \\ 2 &-3x &x-3 \\ -3& 2x &x+2 \end{vmatrix}=0

=> x.(-3x(x+2)-2x(x-3))-(-6)(2.(x+2)-(-3)(x-3))+(-1)(2.2x-(-3)(-3x))

=> x^{3}-7x+6

Root of equation (-3,1,2)

So,

Sum of real root of equation = -3+1+2=0

So, option (2) is correct.


Option 1)

6

Option 2)

0

Option 3)

1

Option 4)

-4

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