Question

What 2 numbers add to give you -2 and multiply to give you -256​

Answer 1

a = -1 + √257 and b = -1 - √257

Explanation:

consider two numbers a and b ,where :

a + b = -2

a × b = -256

Then

b = -a -2

a × b = -256

Then

b = -a -2

a × (-a -2) = -256

Then

b = -a -2

-a² -2a = -256

Then

b = -a -2

a² + 2a - 256 = 0

Solving the equation:

a² + 2a - 256 = 0

The discriminant ∆ = 2² - 4(1)(-256) = 1028

Then

`a = (-2+√(1028) )/(2) = -1 + √(257)`

Or

`a = (-2-√(1028) )/(2) = -1 - √(257)`

Then

b = 1 - √257 - 2 = -1 - √257

Or

b = -1 + √257