Question

If the ratio of the roots of the equation $px^2 + qx + r = 0$ is $a : b$, then $\frac{ab}{\left(a+b\right)^{2}} = $

• A. $\frac{p^{2}}{qr} $
• B. $\frac{pr}{q^{2}} $
• C. $\frac{q^{2}}{pr} $
• D. $\frac{pq}{r^{2}} $

Answer 1

Answer: (B)

Let the roots be $a \alpha$ and $b \alpha$. Then,
$a \alpha+b \alpha=-\frac{q}{p} \text { and } a \alpha \times b \alpha=\frac{r}{p}$
$\therefore \frac{\alpha^{2}(a+b)^{2}}{a b \alpha^{2}}=\frac{q^{2} / p^{2}}{r / p}$
$\Rightarrow \frac{a b}{(a+b)^{2}}=\frac{r p}{q^{2}}$