Question

sum of two integers is minus 2 and their product is minus 35 one of the integer is​

Answer 1

5 and -7.

One integer will be α and other will be β here.

Then, we recall the relation and write quadratic equation

x²-(α+β)x+αβ=0

Since α+β=-2 / αβ=-35

x²+2x-35=0

We use the quadratic formula, $x=\frac{-2\pm\sqrt{4+35\times 4} }{2} =\frac{-2\pm \sqrt{4\times 36} }{2} =\frac{-2\pm 12}{2}$

and α, β will be 5 and -7.

Note

How you solve the equation doesn't matter.

Splitting the terms, formula way,... etc.