If α and β are the zeroes of the polynomial f(y) = y2-p(y+1)+c . . .

Question : If α and β are the zeroes of the polynomial f(y) = y²-p(y+1)+c, such that (α+1)(β+1)=0, then find the value of c.

Doubt by Gauri 

Solution : 

f(y) = y²-p(y+1)+c

f(y) = y²-py-p+c

f(y) = y²-py-(p-c)

A = 1

B = -p

C = -(p-c)

α+β = -B/A
α+β = -(-p)/1

α+β = p

αβ = C/A
αβ = -(p-c)]/1

αβ = -p+c

Now 

(α+1)(β+1)=0
αβ+α+β+1 = 0
αβ+(α+β)+1 = 0
-p+c+p+1 = 0
c+1=0
c=-1

Similar Question : 

⭐ If α and β are the zeroes of the polynomial f(x) = x²-p(x+1)-c, such that (α+1)(β+1)=0, then find the value of c.

Ans : 1