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Q14. If α ,β ...

Question

Q14. If $α, β$ are the zeros of polynomial $f (x)$ $= x^{2} - p (x + 1) - c$ then $(α + 1) (β + 1)$ is equal to:

$c - 1$
$1 - c$
$c$
$1 + c$

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Solution

The correct option is B
$1 - c$

Solution:
Step 1: Relation between zeroes and Coefficient:
Given: $f (x) = x^{2} - p (x + 1) - c$ with zeroes $α a n d β .$
$f (x) = x^{2} - p x - (p + c)$
$s u m o f z e r o e s : a + β = \frac{- (- p)}{1} = p [∵ s u m o f z e r o e s = \frac{- c o e f f i c i e n t o f x}{c o e f f i c i e n t o f x^{2}}]$
$p r o d u c t o f z e r o e s : α β = \frac{- (p + c)}{1} = - (p + c) [∵ p r o d u c t o f z e r o e s = \frac{c o n s t a n t t e r m}{c o e f f i c i e n t o f x^{2}}]$
Step 2: Finding the value of given expression:
$(α + 1) (β + 1) = α β + α + β + 1 = - (p + c) + p + 1 = - p - c + p + 1 = 1 - c$
Final answer: The correct answer is option(B).

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