Q

I have a doubt, kindly clarify. - Matrices and Determinants - JEE Main-4

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

Views

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

=> $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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