TS EAMCET · Maths · Quadratic Equation
If \(\alpha, \beta, \gamma\) are the roots of the equation \(2 x^3+x^2-13 x+6\) \(=0\), then \(\alpha^3+\beta^3+\gamma^3=\)
- A \(-\frac{161}{8}\)
- B 36
- C 99
- D \(-\frac{151}{8}\)
Answer & Solution
Correct Answer
(D) \(-\frac{151}{8}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & 2 x^3+x^2-13 x+6=0 \\ & \alpha+\beta+\gamma=\frac{-1}{2} \\ \Rightarrow & \alpha \beta+\beta \gamma+\gamma \alpha=\frac{-13}{2} \\ \Rightarrow & \alpha \beta \gamma=-3 \Rightarrow \alpha^3+\beta^3+\gamma^3 \\ = &…
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