Q54 / 160 · AP EAMCET 2018 (23 Apr Shift 2) · Mathematics
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 $|p|=$
- A3
- B2
- Correct answerC$\frac{1}{2}$
- D$\frac{1}{3}$
Solution
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 roots $=1$
$$
\Rightarrow \quad p^4 \alpha \beta \gamma \delta=1
$$
...(ii)
From Eqs. (i) and (ii), we are getting
$$
|p|=1 / 2
$$
Hence, the correct answer is option: 'C'.