Algebra 2: Finding real numbers

Question

Find two real numbers whose sum is -9 and product is 24, or show that no such numbers exist.

 

I'm not sure how to calculate this. Thanks in advance for help!

Answer 1

Let x and y be the real numbers. They must sum to -9, so

 

x + y = -9

 

and their product must be 24, so

 

xy= 24

 

Now use one of the equations to remove x, or y, and obtain a single equation with only x, or y. For example,

 

y= -9 - x

and put this into

x (-9-x)=24

which comes to x^2 + 9x + 24 = 0.

 

You must use the quadratic equation to solve, this, and when you do, with a= 1, b=9, and c=24, you will find that

b*b - 4ac is < 0, so there will be no real solution.