y = x^2 + bx + 512 cuts the x axis at (h, 0) and (k, 0). If h and k are integers, what is the least value of b?  Pick:
A) -512
B) -257
C) -256
D) -513
E) 128
As the curve cuts the x-axis at (h,0) and (k,0). Therefore h,k are the roots of the quadratic equation.   For the quadratic equation is in the form of ax^2+bx+c=0,   The product of the roots =c/a= 512/1=256 and the sum of the roots =-b/a=-b   512 can be expressed as product of two numbers in the following ways:   1 * 512   2 * 256   4 * 128   8 * 64   16 *32   The sum of the roots is maximum when the roots are 1 and 256 and the maximum sum is 1 + 512= 
<gadget id="calculator">1 + 512</gadget>
<output>513</output>
513.   The least value possible for b is therefore -513.   -513
<result>D</result>
y = x^2 + bx + 512 cuts the x axis at (h, 0) and (k, 0). If h and k are integers, what is the least value of b?