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The sum of the real roots of the equatio...

The sum of the real roots of the equation
`|{:(x, -6, -1), (2, -3x, x-3), (-3, 2x, x+2):}| = 0,` is equal to

A

6

B

1

C

0

D

`-4`

Text Solution

Verified by Experts

The correct Answer is:
C
`|(x,-6,-1),(2,-3x,x=3),(-3,2x,x+2)|= 0`
`|(x,-6,-1),(2,-3x,x=3),(-5,5x,5)| = 0 rArr |(x,-6,-1),(2,-3x,x-3),(-3,x,1)| =0`
`x(-cancel(3x)-x^(2) + cancel(3x)) + 6(2 + x -3) -1 (2x -3x) = 0`
`-x^(3) + 6x -6 x 0`
`-x^(3) + 7x -6 = 0 rArr x^(3) -7x + 6 = 0 rArr x = 1, 2, -3`
All three real roots s = 0
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