Question

If the ratio of the roots of the equation $p{x}^2+qx+r=0$ is $a:b$, then $\frac{ab}{{(a+b)}^2}$ is equal to

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

Answer 1

The correct option is B $\frac{pr}{q^2}$

Let the roots be $a\alpha$ and $b\alpha$.

Then
$a\alpha +b\alpha =-\frac{q}{p}$ and $a\alpha \times b\alpha =\frac{r}{p}$

$\therefore \frac{{\alpha }^2{(a+b)}^2}{ab{\alpha }^2}=\frac{q^2/p^2}{r/p}$

$\Rightarrow$ $\frac{ab}{{(a+b)}^2}=\frac{rp}{q^2}$