Question

If α and β are the zeros of the quadratic polynomial p(x) = x² -k(x + 1) - a and if (α + 1)(β + 1) = 0, find a.​

Answer 1

p(x) = x² -kx-k-a

sum of the roots p+q = -b/a

= k

product of the roots pq = -(k+a)

(p+1)(q+1) = pq+p+q +1

=k-k-a =0

a=0