AP EAMCET · Maths · Quadratic Equation
\(\alpha, \beta, \gamma\) are the roots of the equation \(x^3-10 x^2+7 x+8=0\). Match the following and choose the correct answer.
| A. \(\alpha+\beta+\gamma\) | (1) \(-\frac{43}{4}\) |
| B. \(\alpha^2+\beta^2+\gamma^2\) | (2) \(-\frac{7}{8}\) |
| C. \(\frac{1}{\alpha}+\frac{1}{\beta}+\frac{1}{\gamma}\) | (3) 86 |
| D. \(\frac{\alpha}{\beta \gamma}+\frac{\beta}{\gamma \alpha}+\frac{\gamma}{\alpha \beta}\) | (4) 0 |
| (5) 10 |
- A \(\begin{array}{cccc}\text { A } & \text { B } & \text { C } & \text { D } \\ 5 & 3 & 1 & 2\end{array}\)
- B \(\begin{array}{cccc}\text { A } & \text { B } & \text { C } & \text { D } \\ 4 & 3 & 1 & 2\end{array}\)
- C \(\begin{array}{cccc}\text { A } & \text { B } & \text { C } & \text { D } \\ 5 & 3 & 2 & 1\end{array}\)
- D \(\begin{array}{cccc}\text { A } & \text { B } & \text { C } & \text { D } \\ 5 & 2 & 3 & 1\end{array}\)
Answer & Solution
Correct Answer
(C) \(\begin{array}{cccc}\text { A } & \text { B } & \text { C } & \text { D } \\ 5 & 3 & 2 & 1\end{array}\)
Step-by-step Solution
Detailed explanation
Since α, β and γ are the roots of the equation \(x^3-10 x^2+7 x+8=0\), then \(\alpha+\beta+\gamma=10 ...(i)\) \(\alpha \beta+\beta \gamma+\gamma \alpha=7 ...(ii)\) \(\alpha \beta \gamma=-8 ...(iii)\) On squaring equation (i) both sides, we get…
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