I think it should be -255.

I think it should be -255.

One of the ways we can find values of a quadratic eqn is by finding the roots.
For a quadratic eqn, sum of roots = -b/a and product of roots = c/a

Here, y=x^2+bx+256 cuts the x axis at (h,0) and (k,0)
Thus, our eqns become: h^2+bh+256=0 and k^2+bk+256=0

Take either eqn, we can write the sum of roots = -b/1 = -b
and product of roots = c/a = 256/1 = 256

Here, roots are 'h' & 'k'; so -
h+k = -b
h*k = 256

256 = 2^8

We can write 256 as a product of roots into powers of 2 as follows -

1*256
2*128
4*64
8*32
16*16

We'll get least values by taking negative values of the above in 'sum of roots' -

-1-256 = -257
-2-128 = -130
-4-64 = -68
-8-32 = -40
-16-16 = -32

We get the minimum as -257
Option(D)

Take either eqn, we can write the sum of roots = -b/1 = -b

We'll get least values by taking negative values of the above in 'sum of roots' -

-1-256 = -257
-2-128 = -130
-4-64 = -68
-8-32 = -40
-16-16 = -32

So, sum of roots is -b = -257. Does it not make b=257?

So, sum of roots is -b = -257. Does it not make b=257?

The Quadratic equation with sum of roots as (a+b) and product of roots as (ab) is
x^2 - (a+b)x + ab = 0

Hence, value of b = -257 and not +257

i dont think this question can be solved in rwo minutes

very lenghty calculation

mohan - You will be able to do it BUT you need to think quick.

y = x^2 + 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?

You needn't always know the formula/e to solve the problem. I will try and solve the problem with out using any formulae.

Since (h,0) and (k,0) lie on the curve y = x^2 + bx + 256, h and k are roots of the equation. So, y can be written in the form (x-h)*(x-k).
y = (x-h)*(x-k) = x^2 + (-h-k)*x + hk = x^2 + bx + 256

Equating the co-efficients of x, we get
(-h-k) = b = -(h+k)
Equating the constants, we get
hk = 256

For b to be minimum, -(h+k) should be minimum.
For (-h-k) to be minimum, h+k should be maximum. We need maximum value h+k where hk = 256

hk = 1*256, h + k = 1 + 256 = 257
hk = 2*128, h + k = 2 + 128 = 130
hk = 4*64, h + k = 4 + 64 = 68
hk = 8*32, h + k = 8 + 32 = 40
hk = 16*16, h + k = 16 + 16 = 32
Never forget to consider the integers on the other side of zero(Though not relevant in this question)
hk = -1*-256, h + k = -1 - 256 = -257
hk = -2*-128, h + k = -2 - 128 = -130
hk = -4*-64, h + k = -4 - 64 = -68
hk = -8*-32, h + k = -8 - 32 = -40
hk = -16*-16, h + k = -16 - 16 = -32.

The highest value of h+k = 257 and the least value of -(h+k) = b = -257.

My GMAT exam scribbling pad would contain just three steps. They are
y = (x-h)*(x-k) = x^2 + bx + 256
b = -(h+k);hk = 256
h = 256 k = 1 -(h+k) = -257