product of 2 consecutive integers n and n+1 is 4556 what are the numbers

Question

Both integers are negative 

Answer 1

Let the two consecutive, negative integers by (n) and (n+1).

 

  (n)(n+1) = 4556

   n² + n - 4556 = 0

 

  Either:

      n = 67     or       n = -68       (either factor or use quadratic formula)

 

  n is negative, so n = -68 

  That means that (n+1) = -67

 

Check:

   Does   (-68)*(-67) = 4556    ?

                 4556 = 4556   ?yes

Answer 2

n(n+1) = 4556

n² + n = 4556

n² + n - 4556 = 0

 

Look for factors of -4556 that add to 1:

 (68)(-67) = -4556, and 68-67 = 1

 

(n+68)(n-67) = 0

n = -68 or n = 67

 

We were told the integers are both negative so n = -68

and n+1 = -67

 

Your integers are -68 and -67

 

Questions?