TS EAMCET · Maths · Quadratic Equation
If \(\alpha, \beta, \gamma\) are the roots of the equation \(x^3-6 x^2+11 x-6=0\) and if \(a=\alpha^2+\beta^2+\gamma^2\), \(b=\alpha \beta+\beta \gamma+\gamma \alpha\) and \(c=(\alpha+\beta)(\beta+\gamma)(\gamma+\alpha)\), then the correct inequality among the following is
- A \(a < b < c\)
- B \(b < a < c\)
- C \(b < c < a\)
- D \(c < a < b\)
Answer & Solution
Correct Answer
(B) \(b < a < c\)
Step-by-step Solution
Detailed explanation
Given equation \(x^3-6 x^2+11 x-6=0\) has the roots \(\alpha, \beta \gamma\). Given, \(\quad a=\alpha^2+\beta^2+\gamma^2\) ...(i) \(b=\alpha \beta+\beta \gamma+\gamma \alpha\) ...(ii) \(c=(\alpha+\beta)(\beta+\gamma)(\gamma+\alpha)\) ...(iii) In cubic equation the sum of the…
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