When y^2+my+2 is divided by y-1, the qoutient is f(y) and the remainder is R1. When y^2+my+2 is divided by y+1, the quotient is g(y) and thr remainder is R2. If R1= R2, then find m.
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You have to apply remainder theorem.
Let p(y)=y^2+my+2.
When p(y) is divided by y-1, then,
y-1=0
,or y=1
Now ,p(1)=1^2 +m×1+2=1+2+m=3+m=R1.
When p(y) is divided by y+1, then,
y+1=0
,or y=(-1)
So, p(-1)=(-1)^2+m×(-1)+2=1-m+2=3-m=R2.
Now,
R1=R2
,or 3+m=3-m
,or 2m=0
,or m=0.(Ans.)
Let p(y)=y^2+my+2.
When p(y) is divided by y-1, then,
y-1=0
,or y=1
Now ,p(1)=1^2 +m×1+2=1+2+m=3+m=R1.
When p(y) is divided by y+1, then,
y+1=0
,or y=(-1)
So, p(-1)=(-1)^2+m×(-1)+2=1-m+2=3-m=R2.
Now,
R1=R2
,or 3+m=3-m
,or 2m=0
,or m=0.(Ans.)
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