Question

If $\alpha$ and $\beta$ are roots of $a{x}^2+bx+c=0$, then equation whose roots are $\frac{\alpha }{\beta },\frac{\beta }{\alpha }$, is

• A. $ac{x}^2+(b^2+2ac)x+ac=0$
• B. $ac{x}^2-(b^2-2ac)x+ac=0$
• C. $bc{x}^2-(b^2-ac)x+ac=0$
• D. None of these

Answer 1

The correct option is B $ac{x}^2-(b^2-2ac)x+ac=0$

Given $\alpha ,\beta$ are roots off $a{x}^2+bx+c=0$
$S=\frac{\alpha }{\beta }+\frac{\beta }{\alpha }=\frac{{\alpha }^2+{\beta }^2}{\alpha \beta }$
$\Rightarrow S=\frac{b^2-2ac}{ac}$
$P=\frac{\alpha }{\beta }\cdot \frac{\beta }{\alpha }=1$
$\therefore$ Required equation is $ac{x}^2-(b^2-2ac)x+ac=0$
Hence, option B.