Question

the sum of two integers is minus 11 and their product is -80 what are the two integers​

Answer 1

$\underline\bold{Question\::}$ The sum of two integers is -11 and their product is -80. What are the two integers?

$\underline\bold{Solution\::}$

$\underline{Let \: the \: two \: integers \: be \: x \: and \: y.}$

The sum of two integers (x and y) is -11.

$\textbf{x + y = -11}$

+ y = - 11 - x

$\textbf{+ y = - (11 + x)}$ ___(eq. 1)

Their (two integers i.e. x and y) product is -80.

[Product means multiply]

$\textbf{xy = - 80}$

x [-(11 + x)] = - 80

x (-11 - x) = - 80

- 11x - x² = - 80

- x² - 11x + 80 = 0

x² + 11x - 80 = 0

x² + 16x - 5x - 80 = 0

x(x + 16) -5(x + 16) = 0

(x + 16) (x - 5) = 0

$\underline{Now \: the \: two \: Cases \: are}$

$Case\:1.$

(x + 16) = 0

x + 16 = 0

x = - 16

$Case\:2.$

(x - 5) = 0

x - 5 = 0

x = + 5

$\underline{\bold{The \: two \: integers \: are \: +5 \: and \: -16}}$