Question

if a-b,a and a+b are zeroes of the polynomial x^3-3x^2+x+1,the value of (a+b) is

Answer 1

The zeroes of the polynomial are (a+b),a, (a-b) 
Let α=a-b
β=a

γ=a+b

α+β+γ=-x² coefficient/x³ coefficient 
a-b+a+a+b=-3/1
3a=-3
a=-3/3
a= -1

αβγ= -constant/x³ coefficient 
(a-b)(a)(a+b)=-1/1
(a²-b²)(a)= -1
[(-1)²-b²](-1)=-1
(1-b²)= -1/-1
1-b²=1
1-1=b²
b²=0
b=√0=0
Therefore, a=-1 and b=0

Hope it helps 

Answer 2

ᴛʜᴇ ᴢᴇʀᴏᴇs ᴏғ ᴛʜᴇ ᴘᴏʟʏɴᴏᴍɪᴀʟ ᴀʀᴇ (ᴀ+ʙ),ᴀ, (ᴀ-ʙ) 
ʟᴇᴛ α=ᴀ-ʙ
β=ᴀ

γ=ᴀ+ʙ

α+β+γ=-x² ᴄᴏᴇғғɪᴄɪᴇɴᴛ/x³ ᴄᴏᴇғғɪᴄɪᴇɴᴛ 
ᴀ-ʙ+ᴀ+ᴀ+ʙ=-3/1
3ᴀ=-3
ᴀ=-3/3
ᴀ= -1

αβγ= -ᴄᴏɴsᴛᴀɴᴛ/x³ ᴄᴏᴇғғɪᴄɪᴇɴᴛ 
(ᴀ-ʙ)(ᴀ)(ᴀ+ʙ)=-1/1
(ᴀ²-ʙ²)(ᴀ)= -1
[(-1)²-ʙ²](-1)=-1
(1-ʙ²)= -1/-1
1-ʙ²=1
1-1=ʙ²
ʙ²=0
ʙ=√0=0
ᴛʜᴇʀᴇғᴏʀᴇ, ᴀ=-1 ᴀɴᴅ ʙ=0

ʜᴏᴘᴇ ɪᴛ ʜᴇʟᴘs