Question

If (y+1) and (y-1) are the factors of p(y)= ay^3+y^2 -2y+b. Find a and b.

Answer 1

Y+1= 0
Y=-1
Now,
Y-1=0
Y=1
First take Y=-1
p(-1)= (a(-1))^3+(-1)^2-2(-1)+b
-a^3 +1 +2+ b=0
-a^3 +b +3 = 0
-a^3+b=-3.......(1)

Now let's take y=1,
p(1)=(a(1))^3+(1)^2-2(1)+b
a^3+1-2+b=0
a^3+b-1=0
a^3+b=1...........(2)
Adding equations 1 and 2
-a^3 +b +a^3+b = -3+1
b+b=-2......(-a^3+a^3 cancel each other)
2b=-2
b= -1........putting this in equation (1)
-a^3+b=-3
-a^3+ -1= -3
-a^3=-2
a^3=2
a= root2



Hope it helps..☺