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JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
The set of all real values of \(\lambda\) for which the quadratic equations, \(\left(\lambda^{2}+1\right) x ^{2}-4 \lambda x +2=0\) always have exactly one root in the interval \((0,1)\) is
- A \((-3,-1)\)
- B \((1,3]\)
- C \((0,2)\)
- D \((2,4]\)
Answer & Solution
Correct Answer
(B) \((1,3]\)
Step-by-step Solution
Detailed explanation
If exactly one root in (0,1) then \(\Rightarrow \quad f (0) \cdot f (1)<0\) \(\Rightarrow \quad 2\left(\lambda^{2}-4 \lambda+3\right)<0\) \(\Rightarrow \quad 1<\lambda<3\) 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)…
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