Determine $p$ and $q$ if $p q = - 24$ and $p + q = 2$

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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,
$x^{2} - (p + q) x + p q = 0$
$\Rightarrow x^{2} - 2 x - 24 = 0$ , substitute the given values
$\Rightarrow x^{2} - 6 x + 4 x - 24 = 0$ , split the middle term
$\Rightarrow (x^{2} - 6 x) + (4 x - 24) = 0$ , group pair of terms
$\Rightarrow x (x - 6) + 4 (x - 6) = 0$ , factor each binomials
$\Rightarrow (x - 6) (x + 4) = 0$ , factor out common factor
$\Rightarrow x = 6$ or $x = - 4$ , set each factor to $0$

Hence $p$ and $q$ are $6$ and $- 4$

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Determine p and q if pq=−24 and p+q=2

Determine $p$ and $q$ if $p q = - 24$ and $p + q = 2$