Question 92349
x^2 + x - k----Quadratic in standard form where:

A=1
B=1
C=k

When we have a quadratic where the A coefficient is equal to 1, then the factors of C must add up to the B coefficient.  For example, lets assume that the factors for your equation are:

(x+a)(x-b)=0 

Expand using the FOIL concept(First, Outer, Inner, Last)

x^2-bx+ax-ab=0  rearrange

x^2+(a-b)x-ab=0--------------eq1

Now in your problem, clearly (a-b) must equal 1

So, if a-b=1 in eq1, then b=(a-1) 

Substitute b=(a-1) into eq1 and rewrite it

x^2+(a-(a-1))x-a(a-1)=0  simplify

x^2+(a-a+1)x-a(a-1)=0 or, further simplifying

x^2+x-a(a-1)=0-----------eq2  Now we know that k=a(a-1) where a has to be greater than or equal to zero.  



Hope this helps--------------ptaylor