Section: Math Section 3

48) If the sum of two numbers is -15 and their product is 56, then these two numbers are roots of which of the following equations?

1. x² + 7x + 8
2. 2x² + 7x + 8
3. x² - 15x + 56
4. x² + 15x + 56
5. None of the above

The sum of two roots of the quadratic equation is the numerical coefficient of the second monomial and the product of the roots is the third monomial.

To solve this problem you have to do the following:

1. Solve for x:
   
   x² + 15x + 56 = 0
   
   
2. Factor the left hand side.
   The left hand side factors into a product with two terms:
   
   (x+7) (x+8) = 0
   
   
3. Solve each term in the product separately.
   Split into two equations:
   
   x+7 = 0 or x+8 = 0
   
   
4. Look at the first equation:
   Solve for x.
   
   Subtract 7 from both sides:
   
   x = -7 or x+8 = 0
   
   
5. Look at the second equation:
   Solve for x.
   Subtract 8 from both sides:
   
   Answer: x = -7 or x = -8