The sum of the real roots of the equatuion

Question:

The sum of the real roots of the equatuion

$\left|\begin{array}{ccc}x & -6 & -1 \\ 2 & -3 x & x-3 \\ -3 & 2 x & x+2\end{array}\right|=0$, is equal to

 

  1. 6

  2. 1

  3. 0

  4. $-4$


Correct Option: , 3

Solution:

By expansion, we get

$-5 x^{3}+30 x-30+5 x=0$

$\Rightarrow-5 x^{3}+35 x-30=0$

$\Rightarrow x^{3}-7 x+6=0$, All roots

So, sum of roots $=0$

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