TS EAMCET · Maths · Quadratic Equation
If \(\alpha, \beta\) are the roots of the equation \(x^2+3 x+\mathrm{k}=0\) and \(\alpha+\frac{1}{\alpha}, \beta+\frac{1}{\beta}\) are the roots of the equation \(4 x^2+p x+18=0\) then k satisfies the equation
- A \(2 x^2-13 x+20=0\)
- B \(x^2-5 x+6=0\)
- C \(2 x^2-7 x+3=0\)
- D \(x^2-8 x+15=0\)
Answer & Solution
Correct Answer
(A) \(2 x^2-13 x+20=0\)
Step-by-step Solution
Detailed explanation
Given: \(x^2+3x+k=0 \Rightarrow \alpha+\beta=-3, \alpha\beta=k\) Given: \(4x^2+px+18=0\) roots are \(\alpha+\frac{1}{\alpha}, \beta+\frac{1}{\beta}\) Product of roots: \(\left(\alpha+\frac{1}{\alpha}\right)\left(\beta+\frac{1}{\beta}\right) = \frac{18}{4} = \frac{9}{2}\)…
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