AP EAMCET · Maths · Quadratic Equation
If \(\alpha, \beta, \gamma\) are the roots of \(x^3-2 x^2+4 x-1=0\) then the equation having the roots \(\beta \gamma+\frac{1}{\alpha}, \alpha \beta+\frac{1}{\gamma}, \gamma \alpha+\frac{1}{\beta}\) is
- A \(x^3+8 x^2-8 x+8=0\)
- B \(x^3-8 x^2+16 x-8=0\)
- C \(x^3-8 x^2+8 x-8=0\)
- D \(x^3-4 x^2+8 x-16=0\)
Answer & Solution
Correct Answer
(C) \(x^3-8 x^2+8 x-8=0\)
Step-by-step Solution
Detailed explanation
\(\alpha+\beta+\gamma = 2\) \(\alpha\beta+\beta\gamma+\gamma\alpha = 4\) \(\alpha\beta\gamma = 1\) New roots are \(y_1 = \beta\gamma + \frac{1}{\alpha}\), \(y_2 = \alpha\beta + \frac{1}{\gamma}\), \(y_3 = \gamma\alpha + \frac{1}{\beta}\). Since \(\alpha\beta\gamma = 1\), then…
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