y = x2 + bx + 256 cuts the x axis at (h, 0) and (k, 0). If h and k are integers, what is the least value of b?
Select the correct option: A) -32 B) -256 C) -255 D) -257 E) 0
Explanatory Answer   The curve cuts the x axis at (h, 0) and (k, 0). So, h and k are the roots of the quadratic equation.   For a quadratic equation of the form ax2 + bx + c = 0, the sum of the roots = -b/a   The sum of the roots of this equation is -b/1 = -b.   Note: Higher the sum of the roots, lower the value of b.   For a quadratic equation of the form ax2 + bx + c = 0, the product of roots = c/a.   Therefore, the product of the roots of this equation = 256/1= 
<gadget id="calculator">256/1</gadget>
<output>256</output>
256.   i.e., h * k= 256   h and k are both integers.   So, h and k are both integral factors of 256.   256 can be expressed as product of two numbers in the following ways:   1 * 256   2 * 128   4 * 64   8 * 32   16 * 16   The sum of the roots is maximum when the roots are 1 and 256 and the maximum sum is 1 + 256= 
<gadget id="calculator">1 + 256</gadget>
<output>257</output>
257.   The least value possible for b is therefore -257.   The correct choice is (-257)
<result>D</result>
y = x2 + bx + 256 cuts the x axis at (h, 0) and (k, 0). If h and k are integers, what is the least value of b?