TS EAMCET · Maths · Quadratic Equation
Let \(\alpha\) be a common root of the equations \(x^3-2 x-25 \lambda=0\), \(3 x^3-8 x-\frac{175}{3} \lambda=0\) and \(\lambda>0\). Then \(\lambda=\)
- A \(\frac{3}{\sqrt{5}}\)
- B \(\frac{\sqrt{3}}{5 \sqrt{5}}\)
- C \(\frac{3}{5 \sqrt{5}}\)
- D \(\frac{3 \sqrt{5}}{5}\)
Answer & Solution
Correct Answer
(C) \(\frac{3}{5 \sqrt{5}}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \lambda=\frac{\alpha^3-2 \alpha}{25} \& \lambda=\frac{9 \alpha^3-24 \alpha}{175} \\ & \Rightarrow \frac{\alpha^3-2 \alpha}{25}=\frac{9 \alpha^3-24 \alpha}{175} \\ & \Rightarrow 7 \alpha^3-14 \alpha=9 \alpha^3-24 \alpha \\ & \Rightarrow 2 \alpha^3-10 \alpha=0 \\…
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