Question

The quadratic in $\log_{2}\left( \frac{2}{3} \right),\mspace{6mu} 1$, such that A.M. of its roots is $2, - 2$ and G.M. is G, is.

• A. $- 2,\mspace{6mu} 1 - \frac{\log 3}{\log 2}$
• B. $\alpha$
• C. $\beta$
• D. None of these

Answer 1

Answer: (A)

$- 2,\mspace{6mu} 1 - \frac{\log 3}{\log 2}$

Answer 2

If $x^{2} + px + 1$ are the roots, then

$a^{2} + c^{2} = - ab$ ⇒$a^{2} - c^{2} = - ab$and $a^{2} - c^{2} = ab$

The required equation is $x,\mspace{6mu} y,\mspace{6mu} z$.