1. Tardigrade
  2. Question
  3. Mathematics
  4. If α, β are roots of the equation textax2+2 x+5=0 then the value of (α-1)(β-1) /[(α+1)(β+1)+(4 / a)] is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

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

Complex Numbers and Quadratic Equations

Solution:

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