TS EAMCET · Maths · Sequences and Series
If the roots of the equation, \(8 x^3+6 p x^2+3 q x-27=0\) are in a geometric progression, then \(q^2+9 p^2+6 p q+q / p=\)
- A -3
- B -10
- C 6
- D 0
Answer & Solution
Correct Answer
(A) -3
Step-by-step Solution
Detailed explanation
Let roots of the equation \(8 x^3+6 p x^2+3 q x-27=0 \text { are } \frac{a}{r}, a, \text { ar. }\) \(\therefore \quad \frac{a}{r}+a+a r=\frac{-6 p}{8}=\frac{-3 p}{4}\) \(\Rightarrow \quad a\left(\frac{1}{r}+1+r\right)=\frac{-3 p}{4}\) \(\ldots\) (i)…
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