Question

The sum of two numbers is 1 but their product is −30. What are they?

Answer 1

Answer:

The two numbers are 6 and -5

Step-by-step explanation:

let the two numbers be x and y

so x+y = 1

and xy = -30

putting the value of y from first equation in the second equation

x(1-x) =  -30

x - x² =  -30

or  x² - x - 30 = 0

using split the middle term method

x² + 5x - 6x - 30 = 0

x(x+5) - 6(x + 5)= 0

(x-6)(x+5) = 0

therefore the two numbers are 6 and -5