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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​

Sagot :

theleangreenbean

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:

  • [tex]ab=-36[/tex]
  • [tex]a+b=5[/tex]

Solving for b

Isolate a in the second equation and solve for b:

[tex]a+b=5\\a=5-b[/tex]

[tex](5-b)b=-36\\5b-b^2=-36[/tex]

Arrange in [tex]ax^2+bx+c=0[/tex] format:

[tex]-b^2+5b+36=0[/tex]

Divide both sides by -1:

[tex]b^2-5b-36=0[/tex]

Factor:

[tex]b^2+4b-9b-36=0\\b(b+4)-9(b-4)=0\\(b-9)(b+4)=0[/tex]

Solve for b using the zero product property:

[tex]b=-4,9[/tex]

Solve for a

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

[tex]a+b=5[/tex]

First, let b = -4:

[tex]a-4=5\\a=9[/tex]

Let b = 9:

[tex]a+9=5\\a=-4[/tex]

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