Multiple choice

If $\alpha$ and $\beta$ are the roots of the equation $x^{2}-p(x+1)-q=0$ then value of $\dfrac { { \alpha }^{ 2 }+2\alpha +1 }{ { \alpha }^{ 2 }+2\alpha +q } +\dfrac { { \beta }^{ 2 }+2{ \beta }+1 }{ { \beta }^{ 2 }+2{ \beta }+q } $

  1. $1$
  2. $2$
  3. $3$
  4. $0$
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A Correct answer
Explanation

Given x^2 - px - p - q = 0, the roots alpha and beta satisfy alpha + beta = p and alpha*beta = -(p+q). Substituting these into the expression and simplifying using the properties of roots, the expression evaluates to 1.

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