Factoring numbers?

Question

What are 2 factors of -1023 that sum up to 2?

Answer 1

A + B = 2
B = 2 - A

A * B = -1023
A(2 - A) = -1023
2A - A^2 = -1023
A^2 - 2A - 1023 = 0

using the quadratic equation

A = (2 +/- sqrt(4 + 4092))/2
= (2 +/- sqrt(4096))/2
= (2 +/- 64)/2
= 1 +/- 32
= 33 and -31

Answer 2

33 and -31.

a*b = -1023
a+b = 2

We can solve for b in the second equation, giving: b = 2-a
Plugging this in as b in the first equation gives:

a(2-a) = -1023
-a^2+2a = -1023
0 = a^2-2a-1023

The quadratic formula gives us a = (2+/-64)/2 = 1+/-32. Or, that a = 33 or a = -31. We know that the two solutions for a are the two numbers by the symmetrical quality of our problem. We could however, verify by using b = 2-a.

That is, when a = 33, b = 2-33 = -31
And when a = -31, b= 2-(-31) = 33

Answer 3

Consider the square root of 1023. The factors must be close to it. One of them must be negative, though

x+y = 2 => y = 2-x
xy = -1023

x(2-x) = -1023

-x^2 + 2x + 1023 = 0

x^2 - 2x - 1023 = 0

x = [2 +/- V (4 + 4092)] / 2 = (2 +/- 64)/2

1 +/- 32 -> 33 and - 31

Ana

Answer 4

If you remember that (x + 1)(x - 1) = x² - 1, this isn't too tough because the difference between those factors is 2.

In your case, you're looking for factors of 1023, which is
(1024) - (1) = (32)² - 1 = (32 + 1)(32 - 1)

I'd go with 33 and -31.

Answer 5

a*b = -1023 eqn 1
a+b = 2 eqn 2
therefore, from eqn 2: a =2-b eqn 3
sub eqn 3 into eqn 1,

b(2-b) = -1023
2b-b^ = -1023

b^-2b-1023 = 0 multiply by '-'
use the quadratic eqn and solve

Answer 6

33, -31

Answer 7

x*y = -1023
x+y = 2
solve for x and y.