Question

What are two numbers that have a product of - 40 and have a sum of 18?

Answer 1

let the numbers be x and y

`xy = - 40 - - - (i) \\ x + y = 18 - - - (ii) \\ from \: (ii) \\ x = 18 - y \\ substitute \: for \: x \: in \: (i) \\ (18 - y)y = - 40 \\ 18y - {y}^(2) = - 40 \\ {y}^(2) - 18y - 40 = 0 \\ use \: the \: quadratic \: equation \: to \: get \: y \\ and \: y \: will \: give \: u \: x`

x = 20

hence y = 18-20

y = -2

or

x = -2

hence y = 18-(-2)

y = 20

The numbers are -2 and 20

Answer 2

Explanation:

xy = -40 and x + y = 18

=> x(18 - x) = -40

=> 18x - x² = -40

=> x² - 18x - 40 = 0

=> (x - 20)(x + 2) = 0

=> x = 20 or x = -2.

The two numbers 20 and -2.