Question

please find the solution

Answer 1

Given :

α and β are the zeroes of x² - p ( x + 1 ) + c

Let f ( x ) = x² - p ( x + 1 ) + c

= > x² - p x - p + c

Comparing with a x² + b x + c

a = 1

b = - p

c = c - p

Given :

( α + 1 )( β + 1 ) = 0

= > αβ + α + β + 1 = 0

We already know that α + β = -b / a

= > α + β = - ( - p ) / 1

= > α + β = p

Also αβ = c / a

= > α + β = ( c - p ) / 1

= > α + β = c - p

Given :

α + β + αβ + 1 = 0

= > p + c - p + 1 = 0

= > c + 1 = 0

= > c = -1

ANSWER :

c = -1

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Answer 2

if there is any doubt plz comment.