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

Answer:

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

Step-by-step 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:

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