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(C) Given the quadratic equation: $x^2 - a(x + 1) - b = 0$Expanding the equation: $x^2 - ax - a - b = 0$Comparing this with the standard form $x^2 - (

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$1 - b$

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(C) Given the quadratic equation: $x^2 - a(x + 1) - b = 0$Expanding the equation: $x^2 - ax - a - b = 0$Comparing this with the standard form $x^2 - (\alpha + \beta)x + \alpha\beta = 0$,we get:Sum of roots: $\alpha + \beta = a$Product of roots: $\alpha\beta = -(a + b)$We need to evaluate: $(\alpha + 1)(\beta + 1)$Expanding the expression: $\alpha\beta + \alpha + \beta + 1$Substituting the values of the sum and product of roots:$= -(a + b) + a + 1$$= -a - b + a + 1$$= 1 - b$

If $\alpha$ and $\beta$ are the roots of the equation $x^2 - a(x + 1) - b = 0$,then $(\alpha + 1)(\beta + 1) = $

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