JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
Let \(\lambda \in R\) and let the equation \(E\) be \(| x |^2-2| x |+|\lambda-3|=0\). Then the largest element in the set \(S =\) \(\{ x +\lambda: x\) is an integer solution of \(E \}\) is \(..........\)
- A \(4\)
- B \(3\)
- C \(5\)
- D \(2\)
Answer & Solution
Correct Answer
(C) \(5\)
Step-by-step Solution
Detailed explanation
\(| x |^2-2| x |+|\lambda-3|=0\) \(| x |^2-2| x |+|\lambda-3|-1=0\) \((| x |-1)^2+|\lambda-3|=1\) At \(\lambda=3, x =0\) and 2 , at \(\lambda=4\) or 2 , then \(x =1 \text { or }-1\) So maximum value of \(x+\lambda=5\)
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