MathDB

Given an expression

x^2 + ax + b

where

a,b

are integer coefficients. At any step, one can change the expression by adding either

1

-1

to only one of the two coefficients

a, b

. a) Suppose that the initial expression has

a =-7

and

b = 19

. Show your modification steps to obtain a new expression that has zero value at some integer value of

x

. b) Starting from the initial expression as above, one gets the expression

x^2 - 17x + 9

after

m

modification steps. Prove that at a certain step

k

with

k < m

, the obtained expression has zero value at some integer value of

x

Problem Statement