AP EAMCET · Maths · Quadratic Equation
If \(\alpha\) and \(\beta\) are the roots of the equation \(2 x^2+6 x+k=0\), then the maximum value of \(\left[\frac{\alpha}{\beta}+\frac{\beta}{\alpha}\right]\) when \(k < 0\) is
- A \(0\)
- B \(1\)
- C \(-1\)
- D \(-2\)
Answer & Solution
Correct Answer
(D) \(-2\)
Step-by-step Solution
Detailed explanation
Given, \(\alpha\) and \(\beta\) are the roots of \(2 x^2+6 x+k=0\) \(\Rightarrow \alpha+\beta=-\frac{6}{2}=-3\) and \(\alpha \beta=\frac{k}{2}\) Now, \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha \beta}\)…
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