Determine $p$ and $q$ is $p q = - 24$ 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 is pq=−24 and p+q=2

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