Question

Hey so I’m making a factoring program and I’m wondering if anyone can give me any ideas on an efficient way to find what two numbers multiple to a specified number, and also add to a specified number.

for example I may have

(a)(b) = 6

a + b = 5

So essentially i just need a way to find the a and b values. In this case they would be 2 and 3.

Can anyone give me any ideas on where to start? Negative numbers must also be considered for use.

Answer 1

There is no need to loop, just use simple math to solve this equation system:

a*b = i;

a+b = j;

a = j/b;

a = i-b;

j/b = i-b; so:

b + j/b + i = 0

b^2 + i*b + j = 0

From here, its a quadratic equation, and it’s trivial to find b (just implement the quadratic equation formula) and from there get the value for a.

There you go:

function finder($add,$product)
{

 $inside_root = $add*$add - 4*$product;

 if($inside_root >=0)
 {

     $b = ($add + sqrt($inside_root))/2;
     $a = $add - $b;

     echo "$a+$b = $add and $a*$b=$product\n";

 }else
 {
   echo "No real solution\n";
 }
}

Real live action:

http://codepad.org/JBxMgHBd