AP EAMCET · Maths · Sequences and Series
If the roots of the equation \(16 x^3-44 x^2+36 x-9=0\) are in harmonic progression, then its greatest root is
- A \(\frac{3}{4}\)
- B \(\frac{3}{2}\)
- C \(\frac{1}{2}\)
- D \(-\frac{1}{2}\)
Answer & Solution
Correct Answer
(B) \(\frac{3}{2}\)
Step-by-step Solution
Detailed explanation
The given equation is \(16 x^3-44 x^2+36 x-9=0\) Let \(\alpha, \beta\) and \(\gamma\) are in H.P. \(\Rightarrow \frac{3}{\beta}=\frac{1}{\alpha}+\frac{1}{\gamma}+\frac{1}{\beta} \Rightarrow \frac{3}{\beta}=\frac{\alpha \beta+\beta \gamma+\gamma \alpha}{\alpha \gamma \beta}\)…
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