TS EAMCET · Maths · Quadratic Equation
Let \(\alpha, \beta, \gamma(\alpha < \beta < \gamma)\) be roots of \(a x^3+b x^2+c x+d=0\) and \(u, v, w(u < v < w)\) be roots of \(a k^3 x^3+b k^2 x^2+c k x+d=0\). If \(\beta^2=\alpha \gamma\), then
- A \(v=\frac{2 v w}{u+w}\)
- B \(2 v=u+w\)
- C \(v^2=u w\)
- D \(v^2=2u w\)
Answer & Solution
Correct Answer
(C) \(v^2=u w\)
Step-by-step Solution
Detailed explanation
\(\because \alpha, \beta\) and \(\gamma\) are the roots of \(a x^3+b x^2+c x+d=0\) and given \(\beta^2=\alpha \gamma\) i.e. \(\alpha, \beta\) and \(\gamma\) are in G.P. So, \(\frac{\alpha}{K}, \frac{\beta}{K}\) and \(\frac{\gamma}{K}\) are also in G.P. Now, \(u, v\) and \(w\)…
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