y = x ^ 2 + bx + 128 cuts the x axis at ( h , 0 ) and ( k , 0 ) . if h and k are integers , what is the least value of b ?
"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 = 128 / 1 = 64 and the sum of the roots = - b / a = - b / 1 128 can be expressed as product of two numbers in the following ways : 1 * 128 2 * 64 4 * 32 8 * 16 the sum of the roots is maximum when the roots are 1 and 128 and the maximum sum is 1 + 128 = 129 . the least value possible for b is therefore - 129 . a"
subtract(negate(128), const_1)