Since, `k^(2)+4k+8, 2k^(2)+3k+6` and `3k^(2) +4k+4` are consecutive terms of an AP.
` :. 2k^(2)+3k+6-(k^(2)+4k+8)=3k^(2)+4k+4-(2k^(2)+3k+6)=` Common difference
`implies 2k^(2)+3k+6-k^(2)-4k-8=3k^(2)+4k+4-2k^(2)-3k-6`
` implies " " k^(2)-k-2=k^(2)+k-2`
`implies " " -k=kimplies2k=0impliesk=0`