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?	Choose the correct choice from the following answers
A) - 512
B) - 257
C) - 256
D) - 513
E) 128

Rationale: 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 = 513 . the least value possible for b is therefore - 513 . d
Answer: D