JEE Mains · Maths · STD 11 - 8. sequence and series
If three distinct number \(a, b, c\) are in \(G.P.\) and the equations \(ax^2 + 2bc + c = 0\) and \(dx^2 + 2ex + f = 0\) have a common root, then which one of the following statements is correct?
- A \(\frac{d}{a},\frac{e}{b},\frac{f}{c}\) are in \(A.P\)
- B \(d, e, f\) are in \(A.P\)
- C \(\frac{d}{a},\frac{e}{b},\frac{f}{c}\) are in \(G.P\)
- D \(d, e, f\) are in \(G.P\)
Answer & Solution
Correct Answer
(A) \(\frac{d}{a},\frac{e}{b},\frac{f}{c}\) are in \(A.P\)
Step-by-step Solution
Detailed explanation
\({b^2} = ac\) Also root of \(a{x^2} + 2bx + c = 0\) are equal \( \Rightarrow x\frac{{ - b}}{a}\) \( \Rightarrow d{\left( {\frac{{ - b}}{a}} \right)^2} + 2e\left( {\frac{{ - b}}{a}} \right) + \int { = 0} \) \(d{b^2} - 2aeb + f{a^2} = 0,{b^2} = ac\)…
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