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4-2.Quadratic Equations and Inequations
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The solution set of the equation $pq{x^2} - {(p + q)^2}x + {(p + q)^2} = 0$ is
A
$\left\{ {\frac{p}{q},\,\frac{q}{p}} \right\}$
B
$\left\{ {pq,\,\frac{p}{q}} \right\}$
C
$\left\{ {\frac{q}{p},\,pq} \right\}$
D
$\left\{ {\frac{{p + q}}{p},\,\frac{{p + q}}{q}} \right\}$
Solution
(d) Given equation $(pq)\,{x^2} – {(p + q)^2}x + {(p + q)^2} = 0$
Let solution set is $\left\{ {\frac{{p + q}}{p},\,\frac{{p + q}}{q}} \right\}$
Sum of roots = $\frac{{{{(p + q)}^2}}}{{pq}}$
==> $\frac{{p + q}}{p} + \frac{{p + q}}{q} = \frac{{{{(p + q)}^2}}}{{pq}}$
Similarly, product of roots = $\frac{{{{(p + q)}^2}}}{{pq}}$
==> $\frac{{p + q}}{p} \times \frac{{p + q}}{q} = \frac{{{{(p + q)}^2}}}{{pq}}$.
Standard 11
Mathematics
