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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^

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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 ${x^2} - (	ext{sum of roots})x + (	ext{product of roots}) = 0$,we get:Sum of roots: $\alpha + \beta = a$Product of roots: $\alpha \beta = -(a + b)$We need to evaluate the expression: $(\alpha + 1)(\beta + 1)$Expanding the expression: $(\alpha + 1)(\beta + 1) = \alpha \beta + \alpha + \beta + 1$Substituting the values of $\alpha + \beta$ and $\alpha \beta$:$= -(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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