Question

If α, β are the zeros of the polynomial f(x) = x² – p (x + 1) – c such that (α + 1) (β + 1) = 0, then c =
A. 1
B. 0
C. – 1
D. 2

Answer 1

Answer:

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Answer 2

$\bf\large\underline\pink{Answer:-}$

C) -1

$\bf\large\underline\blue{Solution:-}$

$\bf\large\underline\green{Step-by-step explanation:-}$

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

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