Question

If α and β are zeroes of the polynomial x² ​​​​​​ - a(x + 1) - b such that (α + 1) ( β + 1) = 0, find the value of b.

Answer 1

Now we know that if α and β are zeroes of polynomial x²-a(x+1)-b then
α+β=a and αβ=(-a-b)
Now (α+1)*(β+1)=0
this means
αβ+(α+β)+1=0
Now substituting value of αβ and α+β from above we get
(a)+(-a-b)+1=0
= a-a-b+1=0
Cancelling a
b=1 (Ans)
Thank you