Determine $p$ and $q$ if $p q = - 12$ 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,
$x^{2} - (p + q) x + p q = 0$
$\Rightarrow x^{2} - 11 x - 12 = 0$ , substitute the given values
$\Rightarrow x^{2} - 12 x + x - 12 = 0$ , split the middle term
$\Rightarrow (x^{2} - 12 x) + (x - 12) = 0$ , group pair of terms
$\Rightarrow x (x - 12) + 1 (x - 12) = 0$ , factor each binomials
$\Rightarrow (x - 12) (x + 1) = 0$ , factor out common factor
$\Rightarrow x = 12$ or $x = - 1$ , set each factor to $0$

Hence $p$ and $q$ are $12$ and $- 1$

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Determine p and q if pq=−12 and p+q=11

Determine $p$ and $q$ if $p q = - 12$ and $p + q = 11$