In the following, you are given the product $p q$ and the sum $p + q$ . Determine $p$ and $q$ :
$p q = - 6$ and $p + q = - 5$

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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,
$x^{2} - (p + q) x + p q = 0$
$\Rightarrow x^{2} + 5 x - 6 = 0$ , substitute the given values
$\Rightarrow x^{2} + 6 x - x - 6 = 0$ , split the middle term
$\Rightarrow (x^{2} + 6 x) + (- x - 6) = 0$ , group pair of terms
$\Rightarrow x (x + 6) - 1 (x + 6) = 0$ , factor each binomials
$\Rightarrow (x + 6) (x - 1) = 0$ , factor out common factor
$\Rightarrow x = - 6$ or $x = 1$ , set each factor to $0$

Hence $p$ and $q$ are $- 6$ and $1$

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Similar questions

In the following, you are given the product pq and the sum p + q, Determine p and q:

(i) pq = 18 and p + q = 11; (ii) pq = 32 and p + q = − 12; (iii) pq = − 24 and p + q = 2; (iv) pq = − 12 and p + q = 11; (v) pq = − 6 and p + q = − 5; (vi) pq = − 44 and p + q = − 7.

Q. Determine

p

and

q

, if

p q = 18

and

p + q = 11

Q. Determine

p

and

q

p q = - 12

and

p + q = 11

Q. Determine

p

and

q

p q = 32

and

p + q = - 12

Q. Determine

p

and

q

p q = - 44

and

p + q = - 7

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In the following, you are given the product pq and the sum p+q. Determine p and q:pq=−6 and p+q=−5

In the following, you are given the product $p q$ and the sum $p + q$ . Determine $p$ and $q$ :
$p q = - 6$ and $p + q = - 5$