Question

3x-2 is a factor of 3x cube + 2x square + px+2, find the value of p

Answer 1

The zero of 3x-2is 2/3
Since 3x-2 is a factor
3x cube +2x square+ px+2=0
3x2/3 cube +2x2/3 square+p2/3+2=0
2/9+8/9+p2/3+2=0
Taking L.C.M of 9,9,3,we get as 9
2+8+6p+18 whole divided by 9=0
Multiplying 9and 0 we get 0
Again carrying 6p in the R.H.S we get -6p
And adding 2,8,18 we get 28
28=-6p
p=28/-6
p=-14/3

Answer 2

3x-2=0
3x=2
x=2/3
∴x=2/3
now,
⇒3x³+2x²+px+2=0
⇒3(2/3)³+2(2/3)²+p×(2/3)+2=0
⇒3×(8/27)+2×(4/9)+2p/3+2=0
⇒24/27+8/9+2p/3+2=0
⇒24+24+18p/27+2=0
⇒24+24+18p+54/27=0
⇒102+18p=0
⇒18p=-102
⇒p=-102/18
⇒p=-17/3