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Relation between Roots and Coefficients for Quadratic

If α and β ar...

Question

If α and β are the roots of the equation $x^{2} - a (x + 1) - b = 0$ , then $(α + 1) (β + 1) =$

A

b

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B

-b

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C

1-b

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D

b-1

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Solution

The correct option is C
1-b

Given equation $x^{2} - a (x + 1) - b = 0$

⇒ $x^{2} - a x - a - b$ ⇒ α + β = α, αβ = -(a + b)

Now $(α + 1) (β + 1) = α β + α + β + 1 = - (a + b) + a + 1 = 1 - b$

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