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
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Mia
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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