The values of `k in R` for which the system of equations `x+k y+3z=0,k x+2y+2z=0,2x+3y+4z=0` admits of nontrivial solution is `2` b. `5//2` c. `3` d. `5//4`

Options

A. 2
B. `5//2`
C. `3`
D. `5//4`

Answer

A, B

Explanation

`|{:(1,,k,,3),(k,,2,,2),(2,,3,,4):}|=0`
`" or " 8+ 4k+9k -12 -4k^(2) -6=0`
`" or " 4k^(2) -13k+10=0`
`" or " 4k^(2) -8k -5k +10=0`
`" or " (2k -5)(k-2) =0`
`" or " k=5//2,2`