Question

If $\left\{ \frac{p - q}{p},\frac{p - q}{q} \right\}$ and $a(x^{2} + 1) - (a^{2} + 1)x = 0$ are the roots of the equation

$a,\frac{1}{a}$ then $a,\frac{1}{2a}$

• A. b
• B. – b
• C. $x^{4} - 8x^{2} - 9 = 0$
• D. $\pm 3,\mspace{6mu} \pm 1$

Answer 1

Answer: (C)

$x^{4} - 8x^{2} - 9 = 0$

Answer 2

Given equation

$\frac{1}{\alpha^{3}} + \frac{1}{\beta^{3}}$

⇒ $- \frac{1}{2}$⇒ $\frac{1}{2}$

Now $\frac{1}{4}$

= $1 + i$.