if alpha and beta are the zeros of the polynomial x square minus 3 into X + 1 – then alpha + 1 into beta + 1 is equal to Question if alpha and beta are the zeros of the polynomial x square minus 3 into X + 1 – then alpha + 1 into beta + 1 is equal to in progress 0 Math Mia 7 months 2021-10-15T20:17:52+00:00 2021-10-15T20:17:52+00:00 1 Answer 0 views 0

## Answers ( )

Answer:

Step-by-step explanation:

Answer:

c = – 1

Step-by-step explanation:

x² – p ( x + 1 ) + c

⇒ x² – p x – p + c

⇒ x² – p x + ( c – p )

Comparing with ax² + bx + c, we get :

a = 1

b = – p

c = c – p .

Given :

( α + 1 )( β + 1 ) = 0

⇒ αβ + α + β + 1 = 0

Note that, sum of roots = – b/a

α + β = – b / a

But b = – p

a = 1

So α + β = – ( – p ) / 1 = p

Product of roots = αβ = c / a

⇒ αβ = ( c – p )

Hence write this as :

αβ + α + β + 1 = 0

⇒ c – p + p + 1 = 0

⇒ c + 1 = 0

⇒ c = -1

Hence, the value of c is – 1