AP EAMCET · Maths · Quadratic Equation
If \(\alpha, \beta, \gamma\), are the roots of the equation \(x^3+4 x+1=0\), then \((\alpha+\beta)^{-1}+(\beta+\gamma)^{-1}+(\gamma+\alpha)^{-1}\) is equal to
- A 2
- B 3
- C 4
- D 5
Answer & Solution
Correct Answer
(C) 4
Step-by-step Solution
Detailed explanation
Since, \(\alpha, \beta, \gamma\) are the roots of the equation \(x^3+4 x+1=0\) \(\therefore \quad \alpha+\beta+\gamma=0\) \(\alpha \beta+\beta \gamma+\gamma \alpha=4\) and \(\quad \alpha \beta \gamma=-1\) \(\therefore(\alpha+\beta)^{-1}+(\beta+\gamma)^{-1}+(\gamma+\alpha)^{-1}\)…
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