Question

If alpha,beta are the zeros of the polynomial x2-px-1)-c such that (alpha + 1)(beta +1)=0,then find the value of c

Answer 1

Given:

x2-(px+1)-c

(α+1)(β+1)=0

to find:

the value of c

as per the question,

(α+1)(β+1)=0

αβ+α+β+1=0

now, sum of roots,

α+β=-b/a

α+β=-(-p) /1

α+β=p

now, product of roots,

αβ=c/a

αβ=c-p

now, αβ+α+β+1=0

c-p+p+1=0

c+1=0

c=-1

✔️Therefore the value of c is -1✔️