Question

Let roots of equation : $ax ^2+ bx + c =0$ are $(\alpha-\beta)$ and $(\gamma-\delta)$ and roots of equation $Ax ^2+ Bx + C =0$ are $(\alpha+\delta)$ and $(\beta+\gamma)$ then $\left|\frac{ a }{ A }\right|$ equals
[Note: $D _1, D _2$ represent discriminants of $ax ^2+ bx + c =0$ and $Ax ^2+ Bx + C =0$ respectively.

• A. $\left|\frac{b}{B}\right|$
• B. $\left|\frac{ c }{ C }\right|$
• C. $\sqrt{\left|\frac{D_1}{D_2}\right|}$
• D. $\sqrt{\left|\frac{D_2}{D_1}\right|}$

Answer 1

Answer: (C)

Difference of roots is same
$\Rightarrow S _1^2-4 P _1= S _2^2-4 P _2 $
$\Rightarrow \frac{ b ^2}{ a ^2}-\frac{4 c }{ a }=\frac{ B ^2}{ A ^2}-\frac{4 C }{ A } $
$\Rightarrow \left(\frac{ a }{ A }\right)^2=\frac{ b ^2-4 ac }{ B ^2-4 AC }=\frac{ D _1}{ D _2}$