MathDB

The operations below can be applied on any expression of the form

ax^2+bx+c

(\text{I})

c \neq 0

, replace

a

4a-\frac{3}{c}

and

c

\frac{c}{4}

(\text{II})

a \neq 0

, replace

a

-\frac{a}{2}

and

c

-2c+\frac{3}{a}

(\text{III}_t)

Replace

x

x-t

, where

t

is an integer. (Different values of

t

can be used.)
Is it possible to transform

x^2-x-6

into each of the following by applying some sequence of the above operations?

(\text{a})

5x^2+5x-1

(\text{b})

x^2+6x+2

Problem Statement