If alpha and beta are zeroes of the polynomial x square - p(x+1)+c such that (alpha+1)(beta+1)=0 find the value of c

Question

Question in more details x2-p(x+1)+c such that (alpha+1)(beta+1)=0 find value of c

Answer 1

Hint: (α+1)(β+1)=0 => α=-1 and β=-1

The polynomial then must be A(x²+2x+1) and that must be identically equal to

x²-px+c-p.. This mean A=1 and you should be able to get the rest from here.