What two numbers have a product of negative 5 and a sum of negative 2?

Answer 1

Let the 2 numbers be 'x' and 'y':

then, x + y = -2

=> x = -2 -y -- (1)

Also, x * y = -5 -- (2)

Put (1) in (2), we have

(-2 -y) * y = -5

-2y -y^2 = -5

y^2 + 2y - 5 = 0

We cannot factorize these numbers easily, so we will have to use the Quadratic Formula to solve this:

y=( -b ± √( b^2 - 4ac )) / ( 2 * a )

=(-2 ± √( 2^2 -4*1*-5 )) / (2 * 1 )

=(-2 ± √(24)) / 2= -1 ± 2 * √(6) / 2=-1 ± √(6)

We can substitute these values into x=-y-2:

x=-(-1 + √(6)) - 2 = 1 - √(6) - 2= -1 - √(6)

x=-(-1 - √(6)) - 2 = 1 + √(6) - 2= -1 + √(6)

Therefore:

x=-1-√(6)

y=-1+√(6)

OR

x=-1+√(6)

y=-1-√(6)