Determine $p$ and $q$ , if $p q = 18$ and $p + q = 11$ .

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Solution

If $p + q$ and $p q$ are known then quadratic equation corresponding to roots as $p$ and $q$ is given by,
$x^{2} - (p + q) x + p q = 0$

Substitute the given values in above equation:
$x^{2} - 11 x + 18 = 0$

Splitting the middle term:
$x^{2} - 9 x - 2 x + 18 = 0$

$(x^{2} - 9 x) + (- 2 x + 18) = 0$
$x (x - 9) - 2 (x - 9) = 0$
$(x - 9) (x - 2) = 0$
$\Rightarrow x = 9$ or $x = 2$

Hence, $p$ and $q$ are $9$ and $2$ .

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Determine p and q, if pq=18 and p+q=11.

Determine $p$ and $q$ , if $p q = 18$ and $p + q = 11$ .