TS EAMCET · Maths · Quadratic Equation
Suppose \(\alpha, \beta, \gamma\) are the roots of \(x^3+x^2+x+2=0\). Then, the value of \(\left(\frac{\alpha+\beta-2 \gamma}{\gamma}\right)\left(\frac{\beta+\gamma-2 \alpha}{\alpha}\right)\left(\frac{\gamma+\alpha-2 \beta}{\beta}\right)\) is
- A \(-\frac{47}{2}\)
- B \(\frac{47}{2}\)
- C -47
- D 47
Answer & Solution
Correct Answer
(A) \(-\frac{47}{2}\)
Step-by-step Solution
Detailed explanation
Since, \(\alpha, \beta, \gamma\) are the roots of \(x^3+x^2+x+2=0\). \[ \therefore \quad \alpha+\beta+\gamma=-1 \] Now, \(\frac{\alpha+\beta-2 \gamma}{\gamma}=\frac{-1-\gamma-2 \gamma}{\gamma}=\frac{-1-3 \gamma}{\gamma}\)…
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