Question

The sum of two integers is -11 and their product is -8o what are the two integers



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Answer 1

Step-by-step explanation:

let two integers are x & y.

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x+y=-11 , y=-11-x

xy=-80

x(-11-x)=-80

-(11x+x^2)=-80

x^2+11x=80

x^2+11x-80=0

x^2+(16-5)x-80=0

x^2+16x-5x-80=0

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

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

x=-16,5

so, y=5,-16

Answer 2

Given :

• The sum of two integers is = -11.
• Their product is = -80.

To find :

• required integer

Step-by-step explanation :

Let x and y be the two numbers

==> xy = -80 .... (1)

==> x + y = -11 .... (2)

by equ(2)

==> x = -11 - y _______(3)

solve for x

so, keep value of x in equ(1)

==> (-11 - y)(y) = -80

==> -11y - y² = -80

rearrange terms

==> y² + 11y - 80 = 0

==> y² - 16y + 5y - 80 = 0

==> y(y - 16) + 5 (y - 16) = 0

==> (y - 16) (y + 5) = 0

Since,

==> y = - 16 or y = 5

Now, for value of x

keep value of y in equ(3)

when,

• y = -16

==> x = -11 - (-16)

==> x = -11 + 16

==> x = 5

when,

• y = 5

==> x = -11 - (5)

==> x = -11 - 5

==> x = -16

Hence,

• Required integer will be 5 , -16 or -16, 5

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