SOLUTION: use a quadratic equation to find two real numbers that satisfy the situation or show that no such numbers exist. " their sum is 2, and their product is -15"

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: use a quadratic equation to find two real numbers that satisfy the situation or show that no such numbers exist. " their sum is 2, and their product is -15"      Log On


   

Question 189415: use a quadratic equation to find two real numbers that satisfy the situation or show that no such numbers exist.
" their sum is 2, and their product is -15"
Answer by solver91311(24713) About Me  (Show Source):
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Find two real numbers such that their sum is 2 and their product is -15.

Let x be one of the numbers and let y be the other, so:



and



Solve both for y:



and



Now that we have two expressions that are each equal to y, set them equal to each other:



Multiply both sides by x:



Add 15 to both sides, multiply by -1, and put into standard form:



Factor:



So:



or






and



So the numbers are -3 and 5.

Check the answer: -3 + 5 = 2, -3 X 5 = -15

John