COMEDK · Maths · 2. Quadratic Equation
If \(\alpha, \beta\) and \(\gamma\) are the roots of the equation \(x^{3}-8 x+8=0\), then \(\Sigma \alpha^{2}\) and \(\Sigma \frac{1}{\alpha \beta}\) are respectively is equal to
- A 16 and 0
- B \(-16\) and 0
- C 16 and 8
- D 0 and \(-16\)
Answer & Solution
Correct Answer
(A) 16 and 0
Step-by-step Solution
Detailed explanation
Since, \(\alpha, \beta\) and \(\gamma\) are the roots of the equation \(x^{3}-8 x+8=0\), then \(\begin{gathered} \alpha+\beta+\gamma=0, \alpha \beta+\beta \gamma+\gamma \alpha=-8 \\ \alpha \beta \gamma=-8 ...(i) \end{gathered}\) Therefore, \((\alpha+\beta+\gamma)^{2}=0\)…
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