SOLUTION: find two integers with a product of -40 and a sum of -3

Algebra.Com
Question 1168261: find two integers with a product of -40 and a sum of -3
Found 2 solutions by VFBundy, ikleyn:
Answer by VFBundy(438)   (Show Source): You can put this solution on YOUR website!
xy = -40
Let y = -40/x

x + y = -3

x - 40/x = -3

x²/x - 40/x = -3

(x² - 40)/x = -3

x² - 40 = -3x

x² + 3x - 40 = 0

(x - 5)(x + 8) = 0

x = 5 and x = -8

If x = 5, y = -8.
If x = -8, y = 5.

So, the two integers are 5 and -8.
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.

ANSWER.  The numbers are -8 and 5.



Two solutions are possible.


One solution is to guess the answer.

A person familiar with the multiplication table, can do it mentally (inside his mind, without using equations) in 5 seconds.



Alternative solution is algebraic.


    x + y = -3     (1)

    xy = -40.      (2)


From equation (1), express  y = -3 - x  and substitute to equation (2)

    x*(-3-x) = -40.


Simplify it and reduce to the standard form of the quadratic equation

    -x^2 - 3x + 40 = 0,   or, equivalently,

     x^2 + 3x - 40 = 0.


You may solve the last equation EITHER factoring

    (x+8)*(x-5) = 0

OR using the quadratic formula

     =  =  = .


It gives you the answer that is placed at the very beginning of my post.

Solved, explained and completed.


RELATED QUESTIONS

are there two integers with a product of -12 and a sum of... (answered by stanbon)
Find two numbers with a sum of 14 and a product of 40 (answered by Alan3354)
Are there two integers with a product of negative 16 and a sum of negative... (answered by richwmiller)
find two polynomials with a sum of degree 3, and with a product of degree 6. (answered by MathLover1)
Two numbers have the sum of -6 and a product of -16. Find the... (answered by drk)
Find a pair of numbers with a sum of 13 and product of... (answered by Alan3354)
the sum of two positive integers is 40. find the two integers such that the product of... (answered by Alan3354)
1.) Two numbers have a sum of 3 and a product of -40. Find the numbers. 2.)... (answered by algebrahouse.com)
The sum of the reciprocals of two consecutive even integers a and b is 9/40 . Find (answered by jrb1965)