AP EAMCET · Maths · Quadratic Equation
If \(\alpha, \beta, \gamma\) are the roots of \(x^3+2 x+5=0\), then \(\sum \frac{\beta+\gamma}{\alpha^2}=\)
- A \(-\frac{2}{5}\)
- B \(\frac{1}{5}\)
- C \(\frac{2}{5}\)
- D \(-\frac{3}{5}\)
Answer & Solution
Correct Answer
(C) \(\frac{2}{5}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text {} \because x^3+2 x+5=0 \\ & \alpha+\beta+\gamma=0 \\ & \alpha \beta+\beta \gamma+\gamma \alpha=2 \\ & \alpha \beta \gamma=-5 \\ & \sum \frac{\beta+\gamma}{\alpha^2}=\frac{\beta+\gamma}{\alpha^2}+\frac{\alpha+\gamma}{\beta^2}+\frac{\alpha+\beta}{\gamma^2}…
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