Mathematics - Quadratic Equation Question with Solution | TestHub

$(x+\lambda {)}^2+1=0$ has clearly imaginary roots

So, both roots of the equations are common

$\therefore \frac{a}{1}=\frac{b}{2\lambda }=\frac{c}{{\lambda }^2+1}=k($ say $)$

Then $\mathrm{a}=\mathrm{k},\mathrm{b}=2\lambda k,\mathrm{c}=\left({\lambda }^2+1\right)\mathrm{k}$

As $\mathrm{a},\mathrm{b},\mathrm{c}$ are sides of triangle

$\begin{array}{rlr}& a+b>c\Rightarrow 2\lambda +1>{\lambda }^2+1\Rightarrow {\lambda }^2-2\lambda <0& \Rightarrow \lambda \in (0,2)\end{array}$

The other conditions also imply same relation.