Question

If $\alpha ,\beta$ are roots of the equation ${\text{ax}}^2+2x+5=0$ then the value of $(\alpha -1)(\beta -1)/[(\alpha +1)(\beta +1)+(4/a)]$ is

• A. $\frac{1}{a+2}$
• B. $a+2$
• C. 1
• D. 2

Answer 1

Answer: (C)

$a{x}^2+2x+5=a(x-\alpha )(x-\beta )$........(i)
Put $x=1\Rightarrow a(1-\alpha )(1-\beta )=a+7$
$x=-1$ $\Rightarrow a(1+\alpha )(1+\beta )=a+3$
$\Rightarrow \frac{(\alpha -1)(\beta -1)}{(\alpha +1)(\beta +1)+\frac{4}{a}}=\frac{\left(\frac{a+7}{a}\right)}{\frac{a+3}{a}+\frac{4}{a}}=1$