if alpha and beta are the zeros of the quadratic polynomial p(x)=x2-k(x+1)-a and if (alpha +1)(beta+1)=0 find a .
Hi Vedant Sharma, let me change alpha as m and beta as n for typing convenience
Let me write the quadratic in right form
x^2 - k x - (k +a) = 0
Now m+n = k
And mn = - (k+a)
Since sum of zeros = - coefficient of x/ coefficient of x^2
Product of zeros = constant term / coefficient of x^2
Given (m+1)(n+1) = 0
==> mn + m + n + 1 = 0
Plugging - (k+a) + k + 1 = 0
Or - k - a + k + 1 = 0
==> a = 1
Let me write the quadratic in right form
x^2 - k x - (k +a) = 0
Now m+n = k
And mn = - (k+a)
Since sum of zeros = - coefficient of x/ coefficient of x^2
Product of zeros = constant term / coefficient of x^2
Given (m+1)(n+1) = 0
==> mn + m + n + 1 = 0
Plugging - (k+a) + k + 1 = 0
Or - k - a + k + 1 = 0
==> a = 1