4.2 Quadratic equations and inequations — ગણિત ધોરણ 11 સાયન્સ — Question

$\Rightarrow \quad f (0) \cdot f (1)<0$

$\Rightarrow \quad 2\left(\lambda^{2}-4 \lambda+3\right)<0$

$\Rightarrow \quad 1<\lambda<3$

Now for $\lambda=1,2 x ^{2}-4 x +2=0$

$(x-1)^{2}=0, x=1,1$

So both roots doesn't lie between (0,1)

$\therefore \lambda \neq 1$

Again for $\lambda=3$

$10 x^{2}-12 x+2=0$

$\Rightarrow \quad x=1, \frac{1}{5}$

so if one root is 1 then second root lie between (0,1)

so $\lambda=3$ is correct.

$\therefore \quad \lambda \in(1,3]$