⇒f(0).f(1)<0 ⇒2(λ2−4λ+3)<0 ⇒1<λ<3 Now for ‌‌λ=1,2x2−4x+2=0 (x−1)2=0,x=1,1 So both roots doesn't lie between (0,1) ∴λ≠1 Again for λ=3 10x2−12x+2=0 ⇒x=1,
1
5
so if one root is 1 then second root lie between (0,1) so λ=3 is correct. ∴λ∈(1,3]