Question

If m and n are zeroes of the polynomial f(x) = x² – p ( x + 1 ) – c then ( m+ 1 )( n+ 1 ) =

Answer 1

Answer:

– ( c + 1 )

Step-by-step explanation:

As m an are zeroes of the polynomial x² – p ( x + 1 ) – c , this means that f(m) and f(n), both are zeroes.

Hence, f(m) = m² – p ( m + 1 ) – c = 0 ------------------ (i)

And,     f(n) = n² – p ( n + 1 ) – c = 0 -------------------(ii)

Equating (i) and (ii), we get

m² – p ( m + 1 ) – c = n² – p ( n + 1 ) – c

∴ m² – p ( m + 1 ) = n² – p ( n + 1 )

∴ m² – p ( m + 1 ) – n² = – p ( n + 1 )

∴ m² – n² = p ( m + 1 ) – p ( n + 1 )

∴ ( m + n )( m – n ) = pm + p – pn – p

∴ ( m + n )( m – n ) = pm – pn

∴ ( m + n )( m – n ) = p( m – n )

∴ ( m + n ) = p

( m+1 )( n+1 )= mn + m + n + 1

                = ( p – n )n + p + 1

                = pn – n² + p + 1

                = – ( n² – ( n + 1 )p + 1 )

                = – ( c + 1 )

Hope it Helped!!!

Please mark as brainliest!!!