JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
If \(\lambda \in R\) is such that the sum of the cubes of the roots of the equation, \(x^2 +(2 - \lambda ) x+ (10 - \lambda ) = 0\) is minimum, then the magnitude of the difference of the roots of this equation is
- A \(20\)
- B \(2\sqrt 5 \)
- C \(2\sqrt 7 \)
- D \(4\sqrt 2 \)
Answer & Solution
Correct Answer
(B) \(2\sqrt 5 \)
Step-by-step Solution
Detailed explanation
Let, the roots of the equation, \(x^{2}+(2-\lambda) x+(10-\lambda)=0\) are \(\alpha\) and \(\beta\). Also roots of the given equation are \(\frac{\lambda-2 \pm \sqrt{4-4 \lambda+\lambda^{2}-40+4 \lambda}}{2}=\frac{\lambda-2 \pm \sqrt{\lambda^{2}-36}}{2}\) The magnitude of the…
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