Question

For the two numbers listed, find two factors of the first number such that their product is the first number and their sum is the second number - 36,5​

Answer 1

The two factors of the first number are -4 and 9.

Explanation:

We're given:

• Two numbers have a product of -36
• The same two numbers have a sum of 5

Let the two numbers be a and b:

• 
  `ab=-36`
• 
  `a+b=5`

Solving for b

Isolate a in the second equation and solve for b:

`a+b=5\\a=5-b`

`(5-b)b=-36\\5b-b^2=-36`

Arrange in
`ax^2+bx+c=0` format:

`-b^2+5b+36=0`

Divide both sides by -1:

`b^2-5b-36=0`

Factor:

`b^2+4b-9b-36=0\\b(b+4)-9(b-4)=0\\(b-9)(b+4)=0`

Solve for b using the zero product property:

`b=-4,9`

Solve for a

Substitute b back into the second equation to solve for a:

`a+b=5`

First, let b = -4:

`a-4=5\\a=9`

Let b = 9:

`a+9=5\\a=-4`