Determine $p$ and $q$ if $p q = - 44$ and $p + q = - 7$

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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,
$x^{2} - (p + q) x + p q = 0$
$\Rightarrow x^{2} + 7 x - 44 = 0$ , substitute the given values
$\Rightarrow x^{2} + 11 x - 4 x - 44 = 0$ , split the middle term
$\Rightarrow (x^{2} + 11 x) + (- 4 x - 44) = 0$ , group pair of terms
$\Rightarrow x (x + 11) - 4 (x + 11) = 0$ , factor each binomials
$\Rightarrow (x + 11) (x - 4) = 0$ , factor out common factor
$\Rightarrow x = - 11$ or $x = 4$ , set each factor to $0$

Hence $p$ and $q$ are $- 11$ and $4$

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Determine p and q if pq=−44 and p+q=−7

Determine $p$ and $q$ if $p q = - 44$ and $p + q = - 7$