SOLUTION: What numbers have a sum of 3 and a product of -180?

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: What numbers have a sum of 3 and a product of -180?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 452589: What numbers have a sum of 3 and a product of -180?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the numbers be j and k
given:
(1) +j+%2B+k+=+3+
(2) +j%2Ak+=+-180+
---------------
(1) +j+%2B+k+=+3+
(1) +k+=+3+-+j+
Substitute this into (2)
(2) +j%2A%28+3-j+%29+=+-180+
(2) +3j+-+j%5E2+=+-180+
(2) +-j%5E2+%2B+3j+%2B+180+=+0+
Solve using the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+-1+
+b+=+3+
+c+=+180+
x+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A%28-1%29%2A180+%29%29%2F%282%2A%28-1%29%29+
x+=+%28-3+%2B-+sqrt%28+9+%2B+720+%29%29%2F%28-2%29+
x+=+%28-3+%2B-+sqrt%28+729+%29%29%2F%28-2%29+
+j+=+%28+-3+-+27+%29+%2F+%28-2%29+
+j+=+%28-30%29%2F%28-2%29+
+j+=+15+
and, since
+j+%2B+k+=+3+
+k+=+3+-+15+
+k+=+-12+
check the answer:
(2) +j%2Ak+=+-180+
(2) +15%2A%28-12%29+=+-180+
(2) +-180+=+-180+
OK
The numbers are 15 and -12