TS EAMCET · Maths · Quadratic Equation
\(\alpha, \beta, \gamma\) are the roots of the equation \(8 x^3-42 x^2+63 x-27=0\) If \(\beta \lt \gamma \lt \alpha\) and \(\beta, \gamma, \alpha\) are in geometric progression, then the extreme value of the expression \(\gamma x^2+4 \beta x+\alpha\) is
- A \(\frac{3}{4}\)
- B 3
- C \(\frac{3}{2}\)
- D \(\frac{21}{4}\)
Answer & Solution
Correct Answer
(C) \(\frac{3}{2}\)
Step-by-step Solution
Detailed explanation
Given equation : \(8 x^3-42 x^2+63 x-27=0\)...(i) \(\alpha, \beta, \gamma\) are root of eqn. (i) \(\gamma^2=\beta \alpha(\beta, \gamma, \alpha \text { in G.P. })\) Sum of root, \(\alpha+\beta+\gamma=\frac{-b}{a}=\frac{42}{8}\)...(ii)…
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