The sum of roots of the equations
`|{:(x+2,,2x+3,,3x+4),(2x+3,,3x+4,,4x+5),(3x+5,,5x+8,,10x+17):}| =0 " is " "____"`

Answer

-4

Explanation

`Delta= |{:(x+2,,2x+3,,3x+4),(2x+3,,3x+4,,4x+5),(3x+5,,5x+8,,10x+17):}|=0`
Applying `R_(3) to R_(3)-R-(2) " and " R_(2) to R_(2) -R_(1)`
`Delta= |{:(x+2,,2x+3,,3x+4),(x+1,,x+1,,x+1),(x+2,,2(x+2),,6(x+2)):}|=0`
`:. Delta =(x+1)(x+2) |{:(x+2,,2x+3,,3x+4),(1,,1,,1),(1,,2,,6):}|=0`
`:. Delta =(x+1)(x+2)[(x+2).4-(2x+3).5+(3x+4).1]`
`=0`
`Delta= (x+1)(x+2)(-3x-3)=0`
`" or " (x+1)^(2)(x+2)=0`
`:. x=-1 ,-1 ,-2`