JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
The value of \(\lambda \) such that sum of the squares of the roots of quadratic equation, \(x^2 + (3 - \lambda )x + 2 = \lambda \) has the lest value is
- A \(\frac{15}{8}\)
- B \(1\)
- C \(\frac{4}{9}\)
- D \(2\)
Answer & Solution
Correct Answer
(D) \(2\)
Step-by-step Solution
Detailed explanation
\(\alpha^{2}+\beta^{2}=(\alpha+\beta)^{2}-2 \alpha \beta\) \(=(3-\lambda)^{2}-2(2-\lambda)\) \(=\lambda^{2}+9-6 \lambda-4+2 \lambda\) \(=\lambda^{2}-4 \lambda+5\) For least value \(\lambda=2\)
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