AP EAMCET · Maths · Quadratic Equation
If the equation whose roots are \(p\) times the roots of \(x^4-2 a x^3+4 b x^2+8 a x+16=0\) is a reciprocal equation, then \(|p|=\)
- A 3
- B 2
- C \(\frac{1}{2}\)
- D \(\frac{1}{3}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
Let the roots are \(\alpha, \beta, \gamma, \delta\) for the equation \[ x^4-2 a x^3+4 b x^2+8 a x+16=0 ...(i) \] So, \[ \alpha \times \beta \times \gamma \times \delta=16 \] For the reciprocal equation roots are \(p \alpha, p \beta, p \gamma\) and \(p \delta\), so product of…
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